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[ { "plaintext": "The flywheel effect is the continuation of oscillations in an oscillator circuit after the control stimulus has been removed. This is usually caused by interacting inductive and capacitive elements in the oscillator. Circuits undergoing such oscillations are said to be flywheeling.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 9920, 8707643, 14896, 4932111 ], "anchor_spans": [ [ 62, 72 ], [ 73, 80 ], [ 164, 173 ], [ 178, 188 ] ] }, { "plaintext": "The flywheel effect may be desirable, such as in phase-locked loops used in synchronous systems, or undesirable, such as in voltage-controlled oscillators.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 24047, 28738, 599563 ], "anchor_spans": [ [ 49, 54 ], [ 76, 87 ], [ 124, 153 ] ] }, { "plaintext": "Flywheel effect is used in Class C modulation where efficiency of modulation can be achieved as high as 90%.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 54005385 ], "anchor_spans": [ [ 27, 34 ] ] }, { "plaintext": "Thermal flywheel effect", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 67046 ], "anchor_spans": [ [ 0, 23 ] ] } ]

[ "Electronic_oscillators" ]

[]

[ { "plaintext": "Foreign exchange service may refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Foreign exchange service (finance)", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 648277 ], "anchor_spans": [ [ 0, 34 ] ] }, { "plaintext": "Foreign exchange service (telecommunications)", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 12693748 ], "anchor_spans": [ [ 0, 45 ] ] } ]

[]

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[ { "plaintext": "Foreign instrumentation signals intelligence, FISINT (Foreign Instrumentation Signature INTelligence) is intelligence from the interception of foreign electromagnetic emissions associated with the testing and operational deployment of foreign aerospace, surface, and subsurface systems. Since it deals with signals that have communicational content, it is a subset of Communications Intelligence (COMINT), which, in turn, is a subset of SIGINT. Unlike general COMINT signals, the content of FISINT signals is not in regular human language, but rather in machine to machine (instrumentation) language or in a combination of regular human language and instrumentation language. FISINT is also considered as a subset of MASINT (measurement and signature intelligence).", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 519276, 29122, 29122, 3867338, 488880 ], "anchor_spans": [ [ 105, 117 ], [ 368, 404 ], [ 437, 443 ], [ 554, 572 ], [ 717, 723 ] ] }, { "plaintext": "Typical examples of such communication include:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Telemetry data (TELINT). Missiles, satellites and other remotely monitored devices often transmit streams of data concerning their location, speed, engine status and other metrics.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 8205729 ], "anchor_spans": [ [ 16, 22 ] ] }, { "plaintext": "Video data links. These may be from UAVs or from satellites used for reconnaissance.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 58900 ], "anchor_spans": [ [ 36, 39 ] ] }, { "plaintext": "Remote access and control transmissions, such as from remote keyless systems and wireless traffic light control systems.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 2109666, 21844439 ], "anchor_spans": [ [ 54, 75 ], [ 90, 111 ] ] }, { "plaintext": "Command signals used in teleoperation, such as the control of aerial vehicles, missiles and remotely-controlled robots.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 1977801, 305100 ], "anchor_spans": [ [ 24, 37 ], [ 92, 118 ] ] }, { "plaintext": "In telecommunication, the term FISINT has the following meanings: ", "section_idx": 1, "section_name": "Telecommunication", "target_page_ids": [ 33094374 ], "anchor_spans": [ [ 3, 20 ] ] }, { "plaintext": "1. Intelligence information derived from electromagnetic emissions associated with the testing and operational deployment of foreign aerospace, surface, and subsurface systems. ", "section_idx": 1, "section_name": "Telecommunication", "target_page_ids": [ 18985062 ], "anchor_spans": [ [ 17, 28 ] ] }, { "plaintext": "2. Technical information and intelligence information derived from the intercept of foreign instrumentation signals by other than the intended recipients. Foreign instrumentation signals intelligence is a category of signals intelligence. ", "section_idx": 1, "section_name": "Telecommunication", "target_page_ids": [ 29122, 29122 ], "anchor_spans": [ [ 72, 81 ], [ 180, 200 ] ] }, { "plaintext": "Foreign instrumentation signals include but are not limited to signals from telemetry, beaconry, electronic interrogators, tracking/fusing/arming/firing command systems, and video data links.", "section_idx": 1, "section_name": "Telecommunication", "target_page_ids": [ 46256, 215461, 32441, 18985040 ], "anchor_spans": [ [ 76, 85 ], [ 153, 160 ], [ 174, 179 ], [ 180, 184 ] ] }, { "plaintext": "SIGINT: Signals intelligence", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 29122 ], "anchor_spans": [ [ 0, 6 ] ] }, { "plaintext": "COMINT: Communications intelligence", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 29122 ], "anchor_spans": [ [ 0, 6 ] ] }, { "plaintext": "ELINT: Electronic intelligence", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 29122 ], "anchor_spans": [ [ 0, 5 ] ] }, { "plaintext": "HUMINT: Human intelligence", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 151848 ], "anchor_spans": [ [ 0, 6 ] ] }, { "plaintext": "IMINT: Imagery intelligence", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 159746 ], "anchor_spans": [ [ 0, 5 ] ] }, { "plaintext": "MASINT: Measurement and signature intelligence", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 488880 ], "anchor_spans": [ [ 0, 6 ] ] }, { "plaintext": "Missile guidance", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 419667 ], "anchor_spans": [ [ 0, 16 ] ] }, { "plaintext": "Intelligence collection management", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 13979372 ], "anchor_spans": [ [ 0, 34 ] ] } ]

[ "Intelligence_gathering_disciplines", "Signals_intelligence", "Applications_of_cryptography" ]

[ "FISINT" ]

[ { "plaintext": "Forward echo: In a transmission line, a reflection propagating in the same direction as the original wave and consisting of energy reflected back by one discontinuity and then forward again by another discontinuity. Forward echoes can be supported by reflections caused by splices or other discontinuities in the transmission medium (e.g. optical fiber, twisted pair, or coaxial tube). In metallic lines, they may be supported by impedance mismatches between the source or load and the characteristic impedance of the transmission medium. They may cause attenuation distortion.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41811, 42728, 33516, 9649, 41812, 3372377, 19042, 320733, 3462904, 40866, 6031554 ], "anchor_spans": [ [ 20, 37 ], [ 41, 51 ], [ 102, 106 ], [ 125, 131 ], [ 315, 334 ], [ 341, 354 ], [ 391, 396 ], [ 432, 452 ], [ 475, 479 ], [ 488, 512 ], [ 557, 579 ] ] }, { "plaintext": " Pre-echo", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 2055507 ], "anchor_spans": [ [ 1, 9 ] ] } ]

[ "Telecommunications_engineering", "Telephony" ]

[]

[ { "plaintext": "In physics, telecommunications, and astronomy, forward scatter is the deflection—by diffraction, nonhomogeneous refraction, or nonspecular reflection by particulate matter of dimensions that are large with respect to the wavelength in question but small with respect to the beam diameter—of a portion of an incident electromagnetic wave, in such a manner that the energy so deflected propagates in a direction that is within 90° of the direction of propagation of the incident wave (i.e., a phase angle greater than 90°). ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 22939, 33094374, 50650, 17318749, 8603, 25948, 521267, 33125, 40780, 9426, 5017866, 3364761, 3169278 ], "anchor_spans": [ [ 3, 10 ], [ 12, 30 ], [ 36, 45 ], [ 70, 80 ], [ 84, 95 ], [ 112, 122 ], [ 139, 149 ], [ 221, 231 ], [ 274, 287 ], [ 316, 336 ], [ 449, 460 ], [ 468, 481 ], [ 491, 502 ] ] }, { "plaintext": "The scattering process may be sensitive to polarization; that is, the polarization of incident waves that are identical in every respect may be scattered differently. Forward scatter differs from backscatter.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 164483, 41564, 863668 ], "anchor_spans": [ [ 4, 14 ], [ 43, 55 ], [ 196, 207 ] ] }, { "plaintext": "Forward scattering can make a back-lit comet appear significantly brighter because the dust and ice crystals are reflecting and enhancing the apparent brightness of the comet by scattering that light towards the observer. Comets studied forward-scattering in visible-thermal photometry include C/1927 X1 (Skjellerup–Maristany), C/1975 V1 (West), and C/1980 Y1 (Bradfield). Comets studied forward-scattering in SOHO non-thermal C3 coronograph photometry include 96P/Machholz and C/2004 F4 (Bradfield). The brightness of the great comets C/2006 P1 (McNaught) and Comet Skjellerup–Maristany near perihelion were enhanced by forward scattering.", "section_idx": 1, "section_name": "Comets", "target_page_ids": [ 223980, 1544902, 592213, 350362, 889722, 8977722, 43882120, 8779868, 1544902, 88213 ], "anchor_spans": [ [ 96, 107 ], [ 294, 326 ], [ 328, 344 ], [ 410, 414 ], [ 430, 441 ], [ 461, 473 ], [ 523, 534 ], [ 536, 545 ], [ 561, 587 ], [ 593, 603 ] ] }, { "plaintext": "Cassini's Views of Saturn's Rings", "section_idx": 3, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Light Scattering Demonstration", "section_idx": 3, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Radio_frequency_propagation", "Scattering,_absorption_and_radiative_transfer_(optics)" ]

[]

[ { "plaintext": "Frequency of optimum transmission (FOT), in the transmission of radio waves via ionospheric reflection, is the highest effective (i.e. working) frequency that is predicted to be usable for a specified path and time for 90% of the days of the month. The FOT is normally just below the value of the maximum usable frequency (MUF). In the prediction of usable frequencies, the FOT is commonly taken as 15% below the monthly median value of the MUF for the specified time and path. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 609152, 15368428, 276281, 10779, 30012, 41359 ], "anchor_spans": [ [ 48, 60 ], [ 64, 69 ], [ 80, 102 ], [ 144, 153 ], [ 210, 214 ], [ 297, 321 ] ] }, { "plaintext": "The FOT is usually the most effective frequency for ionospheric reflection of radio waves between two specified points on Earth. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Synonyms for this term include:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "frequency of optimum traffic", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 43081 ], "anchor_spans": [ [ 21, 28 ] ] }, { "plaintext": "optimum traffic frequency", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "optimum transmission frequency", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "optimum working frequency", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Lowest usable high frequency", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 3182367 ], "anchor_spans": [ [ 0, 28 ] ] }, { "plaintext": "Federal Standard 1037C ", "section_idx": 2, "section_name": "Sources", "target_page_ids": [ 37310 ], "anchor_spans": [ [ 0, 22 ] ] }, { "plaintext": "MIL-STD-188", "section_idx": 2, "section_name": "Sources", "target_page_ids": [ 41882 ], "anchor_spans": [ [ 0, 11 ] ] } ]

[ "Radio_frequency_propagation" ]

[ "FOT" ]

[ { "plaintext": "In telecommunication, a four-wire circuit is a two-way circuit using two paths so arranged that the respective signals are transmitted in one direction only by one path and in the other direction by the other path. The four-wire circuit gets its name from the fact that is uses four conductors to create two complete electrical circuits, one for each direction. The two separate circuits (channels) allow full-duplex operation with low crosstalk.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 346001, 275871, 2112491, 2995499 ], "anchor_spans": [ [ 3, 20 ], [ 55, 62 ], [ 111, 118 ], [ 410, 416 ], [ 436, 445 ] ] }, { "plaintext": "In telephony a four-wire circuit was historically used to transport and switch baseband audio signals in the phone company telephone exchange before the advent of digital modulation and the electronic switching system eliminated baseband audio from the telco plant except for the local loop. The local loop is a two-wire circuit for one reason only: to save copper. Using half the number of copper wire conductors per circuit means that the infrastructure cost for wiring each circuit is halved. Although a lower quality circuit, the local loop allows full duplex operation by using a telephone hybrid to keep near and far voice levels equivalent.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 40773, 26668156, 20637, 41101, 59602, 2139185, 949960 ], "anchor_spans": [ [ 79, 87 ], [ 123, 141 ], [ 163, 181 ], [ 190, 217 ], [ 280, 290 ], [ 312, 328 ], [ 585, 601 ] ] }, { "plaintext": "As the public switched telephone network expanded in size and scope, using many individual wires inside the telco plant became so impractical and labor-intensive that in-office and inter-office signal wiring progressed to high bandwidth coaxial cable (still a popular interconnection method in the 21st century, used with the Lucent 5ESS Class-5 telephone switch to present day), microwave radio relay and ultimately fiber-optic communication for high speed trunk circuits. At the end of the 20th century, four-wire circuits saw renewed growth for corporate local loop service for use in dedicated line service for computer modems to interconnect company computer networks and to connect networks to an Internet service provider for Internet connectivity before commodity DSL and cable modem connectivity was widely available.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 468436, 2049374, 5540651, 7309377, 293860, 4122592, 100245, 41038, 53259 ], "anchor_spans": [ [ 7, 40 ], [ 338, 362 ], [ 380, 401 ], [ 417, 442 ], [ 588, 602 ], [ 655, 672 ], [ 703, 728 ], [ 772, 775 ], [ 780, 791 ] ] }, { "plaintext": " A History of engineering and science in the Bell System : transmission technology (1925-1975)", "section_idx": 1, "section_name": "References", "target_page_ids": [], "anchor_spans": [] } ]

[ "Communication_circuits", "Telephony" ]

[]

[ { "plaintext": "A four-wire terminating set (4WTS) is a balanced transformer used to perform a conversion between four-wire and two-wire operation in telecommunication systems.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 40767, 30906, 41170, 2139185, 33094374 ], "anchor_spans": [ [ 40, 48 ], [ 49, 60 ], [ 98, 107 ], [ 112, 120 ], [ 134, 151 ] ] }, { "plaintext": "For example, a 4-wire circuit may, by means of a 4-wire terminating set, be connected to a 2-wire telephone set. Also, a pair of 4-wire terminating sets may be used to introduce an intermediate 4-wire circuit into a 2-wire circuit, in which loop repeaters may be situated to amplify signals in each direction without positive feedback and oscillation. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41170, 30003, 2139185, 41655, 213354 ], "anchor_spans": [ [ 15, 29 ], [ 98, 107 ], [ 216, 230 ], [ 246, 254 ], [ 317, 334 ] ] }, { "plaintext": "The 4WTS differs from a simple hybrid coil in being equipped to adjust its impedance to maximize return loss.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41246, 41665 ], "anchor_spans": [ [ 31, 42 ], [ 97, 108 ] ] }, { "plaintext": "Four-wire terminating sets were largely supplanted by resistance hybrids in the late 20th century.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] } ]

[ "Telephony_equipment" ]

[]

[ { "plaintext": "A frame is a digital data transmission unit in computer networking and telecommunication. In packet switched systems, a frame is a simple container for a single network packet. In other telecommunications systems, a frame is a repeating structure supporting time-division multiplexing.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 42168, 4122592, 33094374, 43339, 43734, 41796 ], "anchor_spans": [ [ 21, 38 ], [ 47, 66 ], [ 71, 88 ], [ 93, 108 ], [ 161, 175 ], [ 258, 284 ] ] }, { "plaintext": "A frame typically includes frame synchronization features consisting of a sequence of bits or symbols that indicate to the receiver the beginning and end of the payload data within the stream of symbols or bits it receives. If a receiver is connected to the system during frame transmission, it ignores the data until it detects a new frame synchronization sequence.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41176, 15160666 ], "anchor_spans": [ [ 27, 48 ], [ 161, 173 ] ] }, { "plaintext": "In the OSI model of computer networking, a frame is the protocol data unit at the data link layer. Frames are the result of the final layer of encapsulation before the data is transmitted over the physical layer. A frame is \"the unit of transmission in a link layer protocol, and consists of a link layer header followed by a packet.\" Each frame is separated from the next by an interframe gap. A frame is a series of bits generally composed of frame synchronization bits, the packet payload, and a frame check sequence. Examples are Ethernet frames, Point-to-Point Protocol (PPP) frames, Fibre Channel frames, and V.42 modem frames.", "section_idx": 1, "section_name": "Packet switching", "target_page_ids": [ 22747, 41591, 152949, 4269641, 1183889, 43734, 1434110, 9480299, 23511, 13516816, 5419226 ], "anchor_spans": [ [ 7, 16 ], [ 56, 74 ], [ 82, 97 ], [ 143, 156 ], [ 379, 393 ], [ 478, 484 ], [ 500, 520 ], [ 536, 550 ], [ 553, 576 ], [ 591, 610 ], [ 617, 621 ] ] }, { "plaintext": "Often, frames of several different sizes are nested inside each other. For example, when using Point-to-Point Protocol (PPP) over asynchronous serial communication, the eight bits of each individual byte are framed by start and stop bits, the payload data bytes in a network packet are framed by the header and footer, and several packets can be framed with frame boundary octets.", "section_idx": 1, "section_name": "Packet switching", "target_page_ids": [ 23511, 200992, 43734, 78261 ], "anchor_spans": [ [ 96, 119 ], [ 131, 164 ], [ 283, 293 ], [ 359, 380 ] ] }, { "plaintext": "In telecommunications, specifically in time-division multiplex (TDM) and time-division multiple access (TDMA) variants, a frame is a cyclically repeated data block that consists of a fixed number of time slots, one for each logical TDM channel or TDMA transmitter. In this context, a frame is typically an entity at the physical layer. TDM application examples are SONET/SDH and the ISDN circuit-switched B-channel, while TDMA examples are Circuit Switched Data used in early cellular voice services. The frame is also an entity for time-division duplex, where the mobile terminal may transmit during some time slots and receive during others.", "section_idx": 2, "section_name": "Time-division multiplex", "target_page_ids": [ 41796, 31250, 38536, 15231, 959943, 2112491 ], "anchor_spans": [ [ 39, 62 ], [ 73, 102 ], [ 365, 374 ], [ 383, 387 ], [ 440, 461 ], [ 533, 553 ] ] }, { "plaintext": " Datagram", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 40994 ], "anchor_spans": [ [ 1, 9 ] ] }, { "plaintext": " Jumbo frame", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 3960515 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Multiplex techniques", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 41389 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Overhead bit", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 12109789 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": "Ethernet", "section_idx": 4, "section_name": "References", "target_page_ids": [], "anchor_spans": [] } ]

[ "Computer_networks", "Link_protocols", "Packets_(information_technology)", "Units_of_information" ]

[ "data-link frame", "data frame" ]

[ { "plaintext": "Frame rate (expressed in or FPS) is the frequency (rate) at which consecutive images (frames) are captured or displayed. The term applies equally to film and video cameras, computer graphics, and motion capture systems. Frame rate may also be called the , and be expressed in hertz. Frame rate in electronic camera specifications may refer to the maximal possible rate, where, in practice, other settings (such as exposure time) may reduce the frequency to a lower number.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10779, 71925, 2356136, 21555729, 472645, 18567210, 396968, 14121 ], "anchor_spans": [ [ 41, 50 ], [ 79, 84 ], [ 87, 92 ], [ 150, 154 ], [ 159, 171 ], [ 174, 191 ], [ 197, 211 ], [ 277, 282 ] ] }, { "plaintext": "The temporal sensitivity and resolution of human vision varies depending on the type and characteristics of visual stimulus, and it differs between individuals. The human visual system can process 10 to 12 images per second and perceive them individually, while higher rates are perceived as motion. Modulated light (such as a computer display) is perceived as stable by the majority of participants in studies when the rate is higher than 50Hz. This perception of modulated light as steady is known as the flicker fusion threshold. However, when the modulated light is non-uniform and contains an image, the flicker fusion threshold can be much higher, in the hundreds of hertz. With regard to image recognition, people have been found to recognize a specific image in an unbroken series of different images, each of which lasts as little as 13 milliseconds. Persistence of vision sometimes accounts for very short single-millisecond visual stimulus having a perceived duration of between 100ms and 400ms. Multiple stimuli that are very short are sometimes perceived as a single stimulus, such as a 10ms green flash of light immediately followed by a 10ms red flash of light perceived as a single yellow flash of light.", "section_idx": 1, "section_name": "Human vision", "target_page_ids": [ 21280496, 305136, 7677, 407651, 24965027, 23289 ], "anchor_spans": [ [ 43, 55 ], [ 171, 184 ], [ 327, 343 ], [ 507, 531 ], [ 695, 712 ], [ 860, 881 ] ] }, { "plaintext": "Early silent films had stated frame rates anywhere from 16 to 24 frames per second (fps), but since the cameras were hand-cranked, the rate often changed during the scene to fit the mood. Projectionists could also change the frame rate in the theater by adjusting a rheostat controlling the voltage powering the film-carrying mechanism in the projector. Film companies often intended that theaters show their silent films at higher frame rates than they were filmed at. These frame rates were enough for the sense of motion, but it was perceived as jerky motion. To minimize the perceived flicker, projectors employed dual- and triple-blade shutters, so each frame was displayed two or three times, increasing the flicker rate to 48 or 72hertz and reducing eye strain. Thomas Edison said that 46 frames per second was the minimum needed for the eye to perceive motion: \"Anything less will strain the eye.\" In the mid to late 1920s, the frame rate for silent films increased to between 20 and 26FPS.", "section_idx": 2, "section_name": "Film and video", "target_page_ids": [ 26956, 76084, 28412183, 731779, 29778 ], "anchor_spans": [ [ 6, 17 ], [ 266, 274 ], [ 343, 352 ], [ 641, 649 ], [ 769, 782 ] ] }, { "plaintext": "When sound film was introduced in 1926, variations in film speed were no longer tolerated, as the human ear is more sensitive than the eye to changes in frequency. Many theaters had shown silent films at 22 to 26FPS, which is why the industry chose 24FPS for sound films as a compromise. From 1927 to 1930, as various studios updated equipment, the rate of 24FPS became standard for 35mm sound film. At 24FPS, the film travels through the projector at a rate of per second. This allowed simple two-blade shutters to give a projected series of images at 48 per second, satisfying Edison's recommendation. Many modern 35mm film projectors use three-blade shutters to give 72 images per second—each frame is flashed on screen three times.", "section_idx": 2, "section_name": "Film and video", "target_page_ids": [ 70318, 731779 ], "anchor_spans": [ [ 5, 15 ], [ 505, 513 ] ] }, { "plaintext": "In drawn animation, moving characters are often shot \"on twos\", that is to say, one drawing is shown for every two frames of film (which usually runs at 24 frame per second), meaning there are only 12 drawings per second. Even though the image update rate is low, the fluidity is satisfactory for most subjects. However, when a character is required to perform a quick movement, it is usually necessary to revert to animating \"on ones\", as \"twos\" are too slow to convey the motion adequately. A blend of the two techniques keeps the eye fooled without unnecessary production cost.", "section_idx": 2, "section_name": "Film and video", "target_page_ids": [ 498464 ], "anchor_spans": [ [ 9, 18 ] ] }, { "plaintext": "Animation for most \"Saturday morning cartoons\" was produced as cheaply as possible and was most often shot on \"threes\" or even \"fours\", i.e. three or four frames per drawing. This translates to only 8 or 6 drawings per second respectively. Anime is also usually drawn on threes.", "section_idx": 2, "section_name": "Film and video", "target_page_ids": [ 177831, 800 ], "anchor_spans": [ [ 20, 44 ], [ 240, 245 ] ] }, { "plaintext": "Due to the mains frequency of electric grids, analog television broadcast was developed with frame rates of 50Hz (most of the world) or 60Hz (Canada, US, Japan, South Korea). The frequency of the electricity grid was extremely stable and therefore it was logical to use for synchronization.", "section_idx": 2, "section_name": "Film and video", "target_page_ids": [ 488815 ], "anchor_spans": [ [ 11, 26 ] ] }, { "plaintext": "The introduction of color television technology made it necessary to lower that 60FPS frequency by 0.1% to avoid \"dot crawl\", a display artifact appearing on legacy black-and-white displays, showing up on highly-color-saturated surfaces. It was found that by lowering the frame rate by 0.1%, the undesirable effect was minimized.", "section_idx": 2, "section_name": "Film and video", "target_page_ids": [ 1695867 ], "anchor_spans": [ [ 114, 123 ] ] }, { "plaintext": ", video transmission standards in North America, Japan, and South Korea are still based on 60/ 1.001≈59.94 images per second. Two sizes of images are typically used: 1920×1080 (\"1080i/p\") and 1280×720 (\"720p\"). Confusingly, interlaced formats are customarily stated at 1/2 their image rate, 29.97/25FPS, and double their image height, but these statements are purely custom; in each format, 60 images per second are produced. A resolution of 1080i produces 59.94 or 50 1920×540 images, each squashed to half-height in the photographic process and stretched back to fill the screen on playback in a television set. The 720p format produces 59.94/50 or 29.97/25 1280×720p images, not squeezed, so that no expansion or squeezing of the image is necessary. This confusion was industry-wide in the early days of digital video software, with much software being written incorrectly, the developers believing that only 29.97 images were expected each second, which was incorrect. While it was true that each picture element was polled and sent only 29.97 times per second, the pixel location immediately below that one was polled 1/60 of a second later, part of a completely separate image for the next 1/60-second frame.", "section_idx": 2, "section_name": "Film and video", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Film, at its native 24FPS rate could not be displayed without the necessary pulldown process, often leading to \"judder\": To convert 24 frames per second into 60 frames per second, every odd frame is repeated, playing twice, while every even frame is tripled. This creates uneven motion, appearing stroboscopic. Other conversions have similar uneven frame doubling. Newer video standards support 120, 240, or 300 frames per second, so frames can be evenly sampled for standard frame rates such as 24, 48 and 60 FPS film or 25, 30, 50 or 60 FPS video. Of course these higher frame rates may also be displayed at their native rates.", "section_idx": 2, "section_name": "Film and video", "target_page_ids": [ 7508398 ], "anchor_spans": [ [ 76, 84 ] ] }, { "plaintext": "Frame rate in electronic camera specifications may refer to the maximal possible rate, where, in practice, other settings (such as exposure time) may reduce the frequency to a lower number.", "section_idx": 2, "section_name": "Film and video", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Frame rate up-conversion is the process of increasing the temporal resolution of a video sequence by synthesizing one or more intermediate frames between two consecutive frames. A low frame rate causes aliasing, yields abrupt motion artifacts, and degrades the video quality. Consequently, the temporal resolution is an important factor affecting video quality. Algorithms for FRC are widely used in applications, including visual quality enhancement, video compression and slow-motion video generation.", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [ 2771414, 151474 ], "anchor_spans": [ [ 58, 77 ], [ 202, 210 ] ] }, { "plaintext": "Most FRC methods can be categorized into optical flow or kernel-based and pixel hallucination-based methods.", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [ 869825 ], "anchor_spans": [ [ 41, 53 ] ] }, { "plaintext": "Flow-based methods linearly combines predicted optical flows between two input frames to approximate flows from the target intermediate frame to the input frames. They also propose flow reversal (projection) for more accurate image warping. Moreover, there are algorithms that gives different weights of overlapped flow vectors depending on the object depth of the scene via a flow projection layer.", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [ 10403335, 8367 ], "anchor_spans": [ [ 226, 239 ], [ 345, 357 ] ] }, { "plaintext": "Pixel Hallucination-based methods use deformable convolution to the center frame generator by replacing optical flows with offset vectors. There are algorithms that also interpolates middle frames with the help of deformable convolution in the feature domain. However, since these methods directly hallucinate pixels unlike the flow-based FRC methods, the predicted frames tend to be blurry when fast-moving objects are present.", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [ 7519, 173175 ], "anchor_spans": [ [ 49, 60 ], [ 384, 390 ] ] }, { "plaintext": "AviSynth MSU Frame Rate Conversion Filter The AviSynth MSU Frame Rate Conversion Filter is an open-source tool intended for video frame rate up-conversion. It increases the frame rate by an integer factor. It allows, for example, to convert a video with 15 fps into a video with 30 fps.", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [ 59126142 ], "anchor_spans": [ [ 94, 105 ] ] }, { "plaintext": "Adobe Premiere Pro Adobe Premiere Pro is a commercial video editing software program that allows you to slow down your video using optical flow and time remapping effects to conventionally shot footage to create better looking and smoother slow motion.", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Vegas Pro Vegas Pro also is a commercial video editing software program. There is a method to make slow motion video too. To perform it you need to choose the motion magnitude in your video and percentages of playback speed.", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Topaz Video Enhance AI Topaz Video Enhance AI has the Chronos AI model uses deep learning to increase video frame rate without artifacts. This algorithm generates new frames that are often indistinguishable from frames captured in-camera.", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Advanced Frame Rate Converter (AFRC) Main advantage of AFRC algorithm is using of several quality enhancement techniques such as adaptive artifact masking, black stripe processing and occlusion tracking:", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "adaptive artifact masking technique allows to make artifacts less noticeable for eyes thus increasing the integral quality of processed video;", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "black stripe processing allows to avoid artifacts which are commonly appeared in interpolated frames in case of black stripe presented near frame edges;", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "occlusion tracking performs high quality restoration of interpolated frames near edges in case of presence of motion with direction to/from the frame edge.", "section_idx": 3, "section_name": "Frame rate up-conversion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Delta timing", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 25586985 ], "anchor_spans": [ [ 0, 12 ] ] }, { "plaintext": "Federal Standard 1037C", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 37310 ], "anchor_spans": [ [ 0, 22 ] ] }, { "plaintext": "Film-out", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 1342176 ], "anchor_spans": [ [ 0, 8 ] ] }, { "plaintext": "Flicker fusion threshold", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 407651 ], "anchor_spans": [ [ 0, 24 ] ] }, { "plaintext": "Glossary of video terms", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 37583418 ], "anchor_spans": [ [ 0, 23 ] ] }, { "plaintext": "High frame rate", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 37575047 ], "anchor_spans": [ [ 0, 15 ] ] }, { "plaintext": "List of film formats", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 4625137 ], "anchor_spans": [ [ 0, 20 ] ] }, { "plaintext": "Micro stuttering", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 24952549 ], "anchor_spans": [ [ 0, 16 ] ] }, { "plaintext": "MIL-STD-188", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 41882 ], "anchor_spans": [ [ 0, 11 ] ] }, { "plaintext": "Movie projector", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 731779 ], "anchor_spans": [ [ 0, 15 ] ] }, { "plaintext": "Moving image formats", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 3563744 ], "anchor_spans": [ [ 0, 20 ] ] }, { "plaintext": "Time-lapse photography", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 1624732 ], "anchor_spans": [ [ 0, 22 ] ] }, { "plaintext": "Video compression", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 8013 ], "anchor_spans": [ [ 0, 17 ] ] }, { "plaintext": "\"Temporal Rate Conversion\"—a very detailed guide about the visual interference of TV, video & PC", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "(Wayback Machine copy)", "section_idx": 6, "section_name": "External links", "target_page_ids": [ 23538754 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Compare frames per second: which looks better?—a web tool to visually compare differences in frame rate and motion blur.", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Film_and_video_technology", "Temporal_rates" ]

[ "framerate", "frame frequency", "FPS", "frames per second" ]

[ { "plaintext": "The Constitution of the State of Vermont is the fundamental body of law of the U.S. state of Vermont, describing and framing its government. It was adopted in 1793 following Vermont's admission to the Union in 1791 and is largely based upon the 1777 Constitution of the Vermont Republic which was drafted at Windsor in the Old Constitution House and amended in 1786. At 8,295 words, it is the shortest U.S. state constitution.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 18618239, 32578, 15675143, 3963199, 137475, 10482096, 868868 ], "anchor_spans": [ [ 79, 89 ], [ 93, 100 ], [ 125, 139 ], [ 250, 286 ], [ 308, 315 ], [ 323, 345 ], [ 402, 425 ] ] }, { "plaintext": "From 1777 to 1791, Vermont was an independent country, often referred to in the present day as the Vermont Republic. During that time it was usually called the State of Vermont but sometimes called the Commonwealth of Vermont or the Republic of Vermont. Its first constitution, drafted in 1777, was among the most far-reaching in guaranteeing personal freedoms and individual rights. In particular, it banned adult slavery, saying male slaves become free at the age of 21 and females at 18. The 1777 constitution's Declaration of Rights of the Inhabitants of the State of Vermont anticipated the United States Bill of Rights by a dozen years. The first chapter, a \"Declaration of Rights of the Inhabitants of the State of Vermont\", is followed by a \"Plan or Frame of Government\" outlining the structure of governance. It provided that the governor would be elected by the freemen of the state, who could vote regardless of whether they owned property, that each town would be represented in the legislative assembly, that there would be a court of law in each county, and that the legislative assembly and the governor's council would jointly hold legislative power.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 538613 ], "anchor_spans": [ [ 99, 115 ] ] }, { "plaintext": "In 1786, the Constitution was extensively revised to establish a far greater separation of powers than what had prevailed under the 1777 Constitution. In particular, it forbade anyone to simultaneously hold more than one of certain offices, including those of judges, legislators, members of the governor's council, the governor, and the surveyor-general. It also provided that the legislature could no longer function as a court of appeals nor otherwise intervene in cases before the courts, as it had often done.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 28561 ], "anchor_spans": [ [ 77, 97 ] ] }, { "plaintext": "The 1786 Constitution continued in effect when, in 1791, Vermont made the transition from independence to the status of one of the states of the Union. In particular, the governor, the members of the governor's council, and other officers of the state, including judges in all courts, simply continued their terms of office that were already underway.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The 1793 Constitution was adopted two years after Vermont's admission to the Union and continues in effect, with various later amendments, to this day. It eliminated all mention of grievances against King George III and against the State of New York. In 1790, New York's legislature finally renounced its claims that Vermont was a part of New York, the cessation of those claims being effective if and when Congress decided to admit Vermont to the Union.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 30688587, 42029, 8210131 ], "anchor_spans": [ [ 60, 82 ], [ 200, 215 ], [ 241, 249 ] ] }, { "plaintext": "\"In order that the freedom of this Commonwealth may be preserved inviolate\" the 1777 constitution established a Council of Censors. This body consisted of thirteen elected members, chosen every seven years, but not from the Council or General Assembly. They were to check that \"the legislative and executive branches of government have performed their duty as guardians of the people\". They also had the power to call a convention, if needed, to amend the constitution. This council had been based on a similar element of the Pennsylvania Constitution of 1776.", "section_idx": 2, "section_name": "Council of Censors", "target_page_ids": [ 407765 ], "anchor_spans": [ [ 526, 559 ] ] }, { "plaintext": "In 1786, the constitution was amended with language proposed by the 1785 Council of Censors, their first meeting, and adopted by the 1786 Constitutional Convention. The section on the Council of Censors remained generally unchanged, with only an added clarification of scope.", "section_idx": 2, "section_name": "Council of Censors", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In 1793, the constitution was amended with language proposed by the 1792 Council of Censors and adopted by the 1793 Constitutional Convention. The Council now had the \"power to send for persons, papers, and records\".", "section_idx": 2, "section_name": "Council of Censors", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In 1870, the constitution was amended with language proposed by the 1869 Council of Censors, their last meeting, and adopted by the 1870 Constitutional Convention. The Council of Censors was abolished and replaced by a new procedure to amend the constitution.", "section_idx": 2, "section_name": "Council of Censors", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The Vermont Constitution, Chapter 2, Section 72 establishes the procedure for amending the constitution. The Vermont General Assembly, the state's bi-cameral legislature, has the sole power to propose amendments to the Constitution of Vermont. The process must be initiated by a Senate that has been elected in an \"off-year\", that is, an election that does not coincide with the election of the U.S. president. An amendment must originate in the Senate and be approved by a two-thirds vote. It must then receive a majority vote in the House. Then, after a newly elected legislature is seated, the amendment must receive a majority vote in each chamber, first in the Senate, then in the House. The proposed amendment must then be presented to the voters as a referendum and receive a majority of the votes cast.", "section_idx": 3, "section_name": "Amending the constitution", "target_page_ids": [ 426260, 261586, 51582 ], "anchor_spans": [ [ 109, 133 ], [ 201, 211 ], [ 758, 768 ] ] }, { "plaintext": "In 1991 and again in 1993, the Vermont General Assembly approved a constitutional amendment authorizing the justices of the Vermont Supreme Court to revise the Constitution in \"gender-inclusive\" language, replacing gender-specific terms. (Examples: \"men\" and \"women\" were replaced by \"persons\" and the \"Freeman's Oath,\" required of all newly registered voters in the state, was renamed the \"Voters' Oath\"). The revision was ratified by the voters in the general election of November 8, 1994. Vermont is one of six states whose constitutions are written in gender-neutral language.", "section_idx": 4, "section_name": "1990s revision to gender-neutral language", "target_page_ids": [ 11292455 ], "anchor_spans": [ [ 391, 403 ] ] }, { "plaintext": " Council of Censors", "section_idx": 5, "section_name": "See also", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Full text of the Constitution of Vermont", "section_idx": 7, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " The Vermont State Archives text of the Vermont Republic Constitution, 1777", "section_idx": 7, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " The Vermont State Archives text of the 1786 Constitution", "section_idx": 7, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " The Vermont State Archives text of the 1793 Constitution", "section_idx": 7, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Visit the birthplace of Vermont and its Constitution", "section_idx": 7, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " See the original Constitution manuscript", "section_idx": 7, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "1793_in_law", "State_constitutions_of_the_United_States", "Vermont_law", "1793_in_American_politics", "1793_in_Vermont" ]

[]

[ { "plaintext": "In the reception of framed data, a frame slip is the loss of synchronization between a received frame and the receiver clock signal, causing a frame misalignment event, and resulting in the loss of the data contained in the received frame. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 18985040, 28738, 41172, 182693, 62599 ], "anchor_spans": [ [ 27, 31 ], [ 61, 76 ], [ 96, 101 ], [ 119, 131 ], [ 162, 167 ] ] }, { "plaintext": "A frame slip should not be confused with a dropped frame where synchronization is not lost, as in the case of buffer overflow, for example.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 11665297, 4373 ], "anchor_spans": [ [ 8, 12 ], [ 110, 125 ] ] } ]

[ "Synchronization", "Data_transmission" ]

[]

[ { "plaintext": "In telecommunication, frame synchronization or framing is the process by which, while receiving a stream of framed data, incoming frame alignment signals (i.e., a distinctive bit sequences or syncwords) are identified (that is, distinguished from data bits), permitting the data bits within the frame to be extracted for decoding or retransmission.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 41172, 18985040, 3364, 8207914 ], "anchor_spans": [ [ 3, 20 ], [ 108, 114 ], [ 115, 119 ], [ 175, 178 ], [ 192, 200 ] ] }, { "plaintext": "If the transmission is temporarily interrupted, or a bit slip event occurs, the receiver must re-synchronize.", "section_idx": 1, "section_name": "Framing", "target_page_ids": [ 40799 ], "anchor_spans": [ [ 53, 61 ] ] }, { "plaintext": "The transmitter and the receiver must agree ahead of time on which frame synchronization scheme they will use.", "section_idx": 1, "section_name": "Framing", "target_page_ids": [ 28738 ], "anchor_spans": [ [ 73, 88 ] ] }, { "plaintext": "Common frame synchronization schemes are:", "section_idx": 1, "section_name": "Framing", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Framing bit A common practice in telecommunications, for example in T-carrier, is to insert, in a dedicated time slot within the frame, a noninformation bit or framing bit that is used for synchronization of the incoming data with the receiver. In a bit stream, framing bits indicate the beginning or end of a frame. They occur at specified positions in the frame, do not carry information, and are usually repetitive.", "section_idx": 1, "section_name": "Framing", "target_page_ids": [ 33094374, 41779, 41796, 50082 ], "anchor_spans": [ [ 33, 50 ], [ 68, 77 ], [ 108, 117 ], [ 250, 260 ] ] }, { "plaintext": "Syncword framing Some systems use a special syncword at the beginning of every frame.", "section_idx": 1, "section_name": "Framing", "target_page_ids": [ 8207914 ], "anchor_spans": [ [ 44, 52 ] ] }, { "plaintext": "CRC-based framing Some telecommunications hardware uses CRC-based framing.", "section_idx": 1, "section_name": "Framing", "target_page_ids": [ 1711155 ], "anchor_spans": [ [ 56, 73 ] ] }, { "plaintext": "In telemetry applications, a frame synchronizer is used to frame-align a serial pulse code-modulated (PCM) binary stream.", "section_idx": 2, "section_name": "Frame synchronizer", "target_page_ids": [ 46256, 25513330 ], "anchor_spans": [ [ 3, 12 ], [ 102, 105 ] ] }, { "plaintext": "The frame synchronizer immediately follows the bit synchronizer in most telemetry applications. Without frame synchronization, decommutation is impossible.", "section_idx": 2, "section_name": "Frame synchronizer", "target_page_ids": [ 51454127 ], "anchor_spans": [ [ 127, 140 ] ] }, { "plaintext": "The frame synchronization pattern is a known binary pattern which repeats at a regular interval within the PCM stream. The frame synchronizer recognizes this pattern and aligns the data into minor frames or sub-frames. Typically the frame sync pattern is followed by a counter (sub-frame ID) which dictates which minor or sub-frame in the series is being transmitted. This becomes increasingly important in the decommutation stage where all data is deciphered as to what attribute was sampled. Different commutations require a constant awareness of which section of the major frame is being decoded.", "section_idx": 2, "section_name": "Frame synchronizer", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Asynchronous start-stop", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 200992 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Phase synchronization", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 1832436 ], "anchor_spans": [ [ 1, 22 ] ] }, { "plaintext": " Self-synchronizing code", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 41687 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Superframe", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 962123 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " J. L. Massey. \"Optimum frame synchronization \". IEEE trans. comm., com-20(2):115-119, April 1972.", "section_idx": 4, "section_name": "References", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " R Scholtz. \"Frame synchronization techniques\", IEEE Transactions on Communications, 1980.", "section_idx": 4, "section_name": "References", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " P. Robertson. \"Optimal Frame Synchronization for Continuous and Packet Data Transmission\", PhD Dissertation, 1995, Fortschrittberichte VDI Reihe 10, Nr. 376 PDF", "section_idx": 4, "section_name": "References", "target_page_ids": [], "anchor_spans": [] } ]

[ "Data_transmission", "Synchronization" ]

[]

[ { "plaintext": "Framing may refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Framing (construction), common carpentry work", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 2071443 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Framing (law), providing false evidence or testimony to prove someone guilty of a crime", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 726337 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Framing (social sciences)", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10438439 ], "anchor_spans": [ [ 1, 26 ] ] }, { "plaintext": " Framing (visual arts), a technique used to bring the focus to the subject", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 7131114 ], "anchor_spans": [ [ 1, 22 ] ] }, { "plaintext": " Framing (World Wide Web), a technique using multiple panes within a web page", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 1437112 ], "anchor_spans": [ [ 1, 25 ] ] }, { "plaintext": " Pitch framing, a baseball concept", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 11962295 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Timber framing, a traditional method of building with heavy timbers", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 699422 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Frame synchronization, in telecommunications", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 41176 ], "anchor_spans": [ [ 1, 22 ] ] }, { "plaintext": " Frame of reference, a coordinate system", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 74263 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Frame (disambiguation)", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 306880 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Framed (disambiguation)", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 7656369 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Framing device, a narrative tool ", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 659824 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Framework (disambiguation)", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 7965514 ], "anchor_spans": [ [ 1, 27 ] ] }, { "plaintext": " Inertial frame of reference, describes time and space homogeneously, isotropically, independent of time", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 14838 ], "anchor_spans": [ [ 1, 28 ] ] }, { "plaintext": " Picture frame", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 2248824 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Verb framing, in linguistics ", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 435080 ], "anchor_spans": [ [ 1, 13 ] ] } ]

[]

[]

[ { "plaintext": "In telecommunication, the free-space path loss (FSPL) is the attenuation of radio energy between the feedpoints of two antennas that results from the combination of the receiving antenna's capture area plus the obstacle-free, line-of-sight path through free space (usually air). The \"Standard Definitions of Terms for Antennas\", IEEE Std 145-1993, defines \"free-space loss\" as \"The loss between two isotropic radiators in free space, expressed as a power ratio.\" It does not include any power loss in the antennas themselves due to imperfections such as resistance. Free space loss increases with the square of distance between the antennas because the radio waves spread out by the inverse square law and decreases with the square of the wavelength of the radio waves. The FSPL is rarely used standalone, but rather as a part of the Friis transmission formula, which includes the gain of antennas. It is a factor that must be included in the power link budget of a radio communication system, to ensure that sufficient radio power reaches the receiver such that the transmitted signal is received intelligibly.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 40735, 60455, 32502, 41288, 33125, 2404385, 1945347 ], "anchor_spans": [ [ 3, 20 ], [ 61, 72 ], [ 226, 239 ], [ 253, 263 ], [ 688, 706 ], [ 744, 754 ], [ 841, 867 ], [ 957, 968 ] ] }, { "plaintext": "The free-space path loss (FSPL) formula derives from the Friis transmission formula. This states that in a radio system consisting of a transmitting antenna transmitting radio waves to a receiving antenna, the ratio of radio wave power received to the power transmitted is:", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [ 2404385 ], "anchor_spans": [ [ 57, 83 ] ] }, { "plaintext": "where", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the directivity of the transmitting antenna", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [ 4077375 ], "anchor_spans": [ [ 8, 19 ] ] }, { "plaintext": " is the directivity of the receiving antenna", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [ 4077375 ], "anchor_spans": [ [ 8, 19 ] ] }, { "plaintext": " is the signal wavelength", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the distance between the antennas", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The distance between the antennas must be large enough that the antennas are in the far field of each other .", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [ 271708 ], "anchor_spans": [ [ 85, 94 ] ] }, { "plaintext": "The free-space path loss is the loss factor in this equation that is due to distance and wavelength, or in other words, the ratio of power transmitted to power received assuming the antennas are isotropic and have no directivity (): ", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [ 2421481 ], "anchor_spans": [ [ 195, 204 ] ] }, { "plaintext": "Since the frequency of a radio wave is equal to the speed of light divided by the wavelength, the path loss can also be written in terms of frequency: ", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [ 28736 ], "anchor_spans": [ [ 53, 67 ] ] }, { "plaintext": "Beside the assumption that the antennas are lossless, this formula assumes that the polarization of the antennas is the same, that there are no multipath effects, and that the radio wave path is sufficiently far away from obstructions that it acts as if it is in free space. This last restriction requires an ellipsoidal area around the line of sight out to 0.6 of the Fresnel zone be clear of obstructions. The Fresnel zone increases in diameter with the wavelength of the radio waves. Often the concept of free space path loss is applied to radio systems that don't completely meet these requirements, but these imperfections can be accounted for by small constant power loss factors that can be included in the link budget.", "section_idx": 1, "section_name": "Free-space path loss formula", "target_page_ids": [ 41564, 41385, 41196, 1945347 ], "anchor_spans": [ [ 84, 96 ], [ 144, 153 ], [ 370, 382 ], [ 717, 728 ] ] }, { "plaintext": "The free-space loss increases with the distance between the antennas and decreases with the wavelength of the radio waves due to these factors:", "section_idx": 2, "section_name": "Influence of distance and frequency", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Intensity () – the power density of the radio waves decreases with the square of distance from the transmitting antenna due to spreading of the electromagnetic energy in space according to the inverse square law", "section_idx": 2, "section_name": "Influence of distance and frequency", "target_page_ids": [ 41993, 2207861, 41288 ], "anchor_spans": [ [ 0, 9 ], [ 19, 32 ], [ 193, 211 ] ] }, { "plaintext": "Antenna capture area () – the amount of power the receiving antenna captures from the radiation field is proportional to a factor called the antenna aperture or antenna capture area, which increases with the square of wavelength. Since this factor is not related to the radio wave path but comes from the receiving antenna, the term \"free-space path loss\" is a little misleading.", "section_idx": 2, "section_name": "Influence of distance and frequency", "target_page_ids": [ 1470583 ], "anchor_spans": [ [ 0, 20 ] ] }, { "plaintext": "Directivity of receiving antenna- while the above formulas are correct, the presence of Directivities Dt and Dr builds the wrong intuition in the FSPL Friis transmission formula. The formula seems to say that \"free space path loss\" increases with frequency in vacuum, which is misleading. The frequency dependence of path loss does not come from free space propagation, but rather from receiving antenna capture area frequency dependence. As frequency increases, the directivity of an antenna of a given physical size will increase. In order to keep receiver antenna directivity constant in the formula, the antenna size must be reduced, and a smaller size antenna results in less power being received as it is able to capture less power with a smaller area. In other words, the path loss increases with frequency because the antenna size is reduced to keep directivity constant in the formula, and has nothing to do with propagation in vacuum. ", "section_idx": 2, "section_name": "Influence of distance and frequency", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Directivity of transmitting antenna - the directivity of transmitting antenna does not have the same role as directivity of receiving antenna. The difference is that the receiving antenna is receiving the power from free space, and hence captures less power as it becomes smaller. The transmitting antenna does not transmit less power as it becomes smaller (for example half wave dipole), because it is receiving its RF power from a generator or source, and if the source is 1 Watt or Pt, the antenna will transmit all of it (assuming ideal efficiency and VSWR for simplicity).", "section_idx": 2, "section_name": "Influence of distance and frequency", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The radio waves from the transmitting antenna spread out in a spherical wavefront. The amount of power passing through any sphere centered on the transmitting antenna is equal. The surface area of a sphere of radius is . Thus the intensity or power density of the radiation in any particular direction from the antenna is inversely proportional to the square of distance ", "section_idx": 3, "section_name": "Derivation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For an isotropic antenna which radiates equal power in all directions, the power density is evenly distributed over the surface of a sphere centered on the antenna", "section_idx": 3, "section_name": "Derivation", "target_page_ids": [ 2421481 ], "anchor_spans": [ [ 7, 24 ] ] }, { "plaintext": "The amount of power the receiving antenna receives from this radiation field is ", "section_idx": 3, "section_name": "Derivation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The factor , called the effective area or aperture of the receiving antenna, which has the units of area, can be thought of as the amount of area perpendicular to the direction of the radio waves from which the receiving antenna captures energy. Since the linear dimensions of an antenna scale with the wavelength , the cross sectional area of an antenna and thus the aperture scales with the square of wavelength . The effective area of an isotropic antenna (for a derivation of this see antenna aperture article) is ", "section_idx": 3, "section_name": "Derivation", "target_page_ids": [ 1470583 ], "anchor_spans": [ [ 490, 506 ] ] }, { "plaintext": "Combining the above (1) and (2), for isotropic antennas", "section_idx": 3, "section_name": "Derivation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A convenient way to express FSPL is in terms of decibels (dB):", "section_idx": 4, "section_name": "Free-space path loss in decibels", "target_page_ids": [ 8410 ], "anchor_spans": [ [ 48, 55 ] ] }, { "plaintext": "using SI units of meters for , Hertz (s−1) for , and meters per second (m⋅s−1) for .", "section_idx": 4, "section_name": "Free-space path loss in decibels", "target_page_ids": [ 26764, 14121 ], "anchor_spans": [ [ 6, 13 ], [ 31, 36 ] ] }, { "plaintext": "For typical radio applications, it is common to find measured in kilometers and in gigahertz, in which case the FSPL equation becomes", "section_idx": 4, "section_name": "Free-space path loss in decibels", "target_page_ids": [ 50510, 14121 ], "anchor_spans": [ [ 66, 76 ], [ 85, 94 ] ] }, { "plaintext": "an increase of 240dB, because the units increase by factors of and respectively, so:", "section_idx": 4, "section_name": "Free-space path loss in decibels", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For in kilometers and megahertz respectively, the constant becomes .", "section_idx": 4, "section_name": "Free-space path loss in decibels", "target_page_ids": [ 14121 ], "anchor_spans": [ [ 23, 32 ] ] }, { "plaintext": "For in meters and megahertz respectively, the constant becomes .", "section_idx": 4, "section_name": "Free-space path loss in decibels", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For in meters and kilohertz respectively, the constant becomes .", "section_idx": 4, "section_name": "Free-space path loss in decibels", "target_page_ids": [ 14121 ], "anchor_spans": [ [ 19, 28 ] ] }, { "plaintext": "Computation of radiowave attenuation in the atmosphere", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 29082171 ], "anchor_spans": [ [ 0, 54 ] ] }, { "plaintext": "Friis transmission equation", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 2404385 ], "anchor_spans": [ [ 0, 27 ] ] }, { "plaintext": "Radio propagation model", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 271195 ], "anchor_spans": [ [ 0, 23 ] ] }, { "plaintext": "ITU-R P.525", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 26177291 ], "anchor_spans": [ [ 0, 11 ] ] }, { "plaintext": "Link budget", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 1945347 ], "anchor_spans": [ [ 0, 11 ] ] }, { "plaintext": "Two-ray ground reflection model", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 40480268 ], "anchor_spans": [ [ 0, 31 ] ] }, { "plaintext": "Derivation of the dB version of the Path Loss Equation", "section_idx": 7, "section_name": "Further reading", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Path loss Pages for free space and real world – includes free space loss calculator", "section_idx": 7, "section_name": "Further reading", "target_page_ids": [], "anchor_spans": [] } ]

[ "Telecommunications_engineering", "Radio_frequency_propagation_model" ]

[]

[ { "plaintext": "Freeze frame television is television in which the frames of the video are transmitted as a sequence of still images at a rate far too slow to be perceived as continuous motion by human vision. The receiving device typically displays each frame until the next complete frame is available.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 29831, 2356136 ], "anchor_spans": [ [ 27, 37 ], [ 51, 56 ] ] }, { "plaintext": "For an image of specified quality, e.g., resolution and color depth, freeze-frame television has a lower bandwidth requirement than that of full-motion television. For this reason, NASA, which refers to this technique as sequential still video, uses it on UHF when Ku band full-motion video signals are not available.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 1191184, 331448, 15612827, 18426568, 160501, 77786 ], "anchor_spans": [ [ 41, 51 ], [ 56, 67 ], [ 105, 114 ], [ 182, 186 ], [ 257, 260 ], [ 266, 273 ] ] }, { "plaintext": "Slow-scan television", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 51210 ], "anchor_spans": [ [ 0, 20 ] ] }, { "plaintext": "Narrowband television", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 1376779 ], "anchor_spans": [ [ 0, 21 ] ] } ]

[ "Film_and_video_technology" ]

[]

[ { "plaintext": "The F region of the ionosphere is home to the F layer of ionization, also called the Appleton–Barnett layer, after the English physicist Edward Appleton and New Zealand physicist and meteorologist Miles Barnett. As with other ionospheric sectors, 'layer' implies a concentration of plasma, while 'region' is the volume that contains the said layer. The F region contains ionized gases at a height of around 150–800km (100 to 500 miles) above sea level, placing it in the Earth's thermosphere, a hot region in the upper atmosphere, and also in the heterosphere, where chemical composition varies with height. Generally speaking, the F region has the highest concentration of free electrons and ions anywhere in the atmosphere. It may be thought of as comprising two layers, the F1 and F2 layers.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 15097, 396514, 34678990, 25916521, 47463, 202899, 1681644, 9476, 18963787 ], "anchor_spans": [ [ 20, 30 ], [ 137, 152 ], [ 197, 210 ], [ 282, 288 ], [ 479, 491 ], [ 519, 529 ], [ 547, 559 ], [ 679, 688 ], [ 693, 697 ] ] }, { "plaintext": "The F-region is located directly above the E region (formerly the Kennelly-Heaviside layer) and below the protonosphere. It acts as a dependable reflector of HF radio signals as it is not affected by atmospheric conditions, although its ionic composition varies with the sunspot cycle. It reflects normal-incident frequencies at or below the critical frequency (approximately 10MHz) and partially absorbs waves of higher frequency.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 17004, 15985775, 40975 ], "anchor_spans": [ [ 43, 51 ], [ 106, 119 ], [ 342, 360 ] ] }, { "plaintext": "The F1 layer is the lower sector of the F layer and exists from about 150 to 220km (100 to 140 miles) above the surface of the Earth and only during daylight hours. It is composed of a mixture of molecular ions O2+ and NO+, and atomic ions O+. Above the F1 region, atomic oxygen becomes the dominant constituent because lighter particles tend to occupy higher altitudes above the turbopause (at ~100km, 60 miles). This atomic oxygen provides the O+ atomic ions that make up the F2 layer.", "section_idx": 1, "section_name": "F1 and F2 layers", "target_page_ids": [ 18963787, 3966381 ], "anchor_spans": [ [ 206, 210 ], [ 380, 390 ] ] }, { "plaintext": "The F1 layer has approximately 5 × 105 e/cm3 (free electrons per cubic centimeter) at noontime and minimum sunspot activity, and increases to roughly 2 × 106 e/cm3 during maximum sunspot activity. The density falls off to below 104 e/cm3 at night.", "section_idx": 1, "section_name": "F1 and F2 layers", "target_page_ids": [ 27616 ], "anchor_spans": [ [ 107, 114 ] ] }, { "plaintext": " The F1 layer merges into the F2 layer at night.", "section_idx": 1, "section_name": "F1 and F2 layers", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Though fairly regular in its characteristics, it is not observable everywhere or on all days. The principal reflecting layer during the summer for paths of 2,000 to 3,500km (1200 to 2200 miles) is the F1 layer. However, this depends upon the frequency of a propagating signal. The E layer electron density and resultant MUF, maximum usable frequency, during high solar activity periods can refract and thus block signals of up to about 15MHz from reaching the F1 and F2 regions, with the result that distances are much shorter than possible with refractions from the F1 and F2 regions. But extremely low radiation-angle signals (lower than about 6degrees) can reach distances of 3000km (1900 miles) via Eregion refractions.", "section_idx": 1, "section_name": "F1 and F2 layers", "target_page_ids": [ 41359 ], "anchor_spans": [ [ 326, 350 ] ] }, { "plaintext": " The F2 layer exists from about 220 to 800km (140 to 500 miles) above the surface of the Earth. The F2 layer is the principal reflecting layer for HF communications during both day and night. The horizon-limited distance for one-hop F2 propagation is usually around 4,000km (2500 miles). The F2 layer has about 106 e/cm3. However, variations are usually large, irregular, and particularly pronounced during magnetic storms. The F layer behaviour is dominated by the complex thermospheric winds.", "section_idx": 1, "section_name": "F1 and F2 layers", "target_page_ids": [ 33094374, 55184, 271195 ], "anchor_spans": [ [ 150, 164 ], [ 229, 232 ], [ 236, 247 ] ] }, { "plaintext": "Critical F2 layer frequencies are the ones that will not go through the F2 layer. Under rare atmospheric conditions, F2 propagation can occur, resulting in VHF television and FM radio signals being received over great distances, well beyond the normal reception area. ", "section_idx": 2, "section_name": "Usage in radio communication", "target_page_ids": [ 14393992, 69480 ], "anchor_spans": [ [ 117, 131 ], [ 156, 159 ] ] }, { "plaintext": "Ионосфера", "section_idx": 3, "section_name": "References", "target_page_ids": [], "anchor_spans": [] } ]

[ "Ionosphere", "Radio_frequency_propagation" ]

[]

[ { "plaintext": "In telecommunication, the term frequency averaging has the following meanings: ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374 ], "anchor_spans": [ [ 3, 20 ] ] }, { "plaintext": "The process by which the relative phases of precision clocks are compared for the purpose of defining a single time standard. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41932, 41799 ], "anchor_spans": [ [ 44, 53 ], [ 111, 124 ] ] }, { "plaintext": "A process in which network synchronization is achieved by use, at all nodes, of oscillators that adjust their frequencies to the average frequency of the digital bit streams received from connected nodes. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 46545, 28738, 10779, 8276, 3364 ], "anchor_spans": [ [ 19, 26 ], [ 27, 42 ], [ 137, 146 ], [ 154, 161 ], [ 162, 165 ] ] }, { "plaintext": "In frequency averaging, all oscillators are assigned equal weight in determining the ultimate network frequency. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In terms of musical note frequency, the averaging of the frequency of low or high notes in a solo instrumental piece is a technique used to match different instruments together so they may be played together. The musical note frequency calculation formula is used: F=(2^12/n)*440, where n equals the number of positive or negative steps away from the base note of A4(440 hertz) and F equals the frequency. The formula is used in calculating the frequency of each note in the piece. The values are then added together and divided by the number of notes. This is the average frequency of those notes. It is said that such techniques were used by classical composers, especially those who involved mathematics heavily in their music. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] } ]

[ "Telecommunications_techniques", "Synchronization", "Frequency-domain_analysis" ]

[]

[ { "plaintext": "In telecommunication, frequency-change signaling is a telegraph signaling method in which one or more particular frequencies correspond to each desired signaling condition of a telegraph code. The transition from one set of frequencies to the other may be a continuous or a discontinuous change in the frequency or phase.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 30010, 41703, 10779, 5225, 10779, 24047 ], "anchor_spans": [ [ 3, 20 ], [ 55, 64 ], [ 65, 74 ], [ 114, 125 ], [ 188, 192 ], [ 304, 313 ], [ 317, 322 ] ] }, { "plaintext": "Frequency-shift keying", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 41193 ], "anchor_spans": [ [ 0, 22 ] ] }, { "plaintext": "Frequency modulation", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 10835 ], "anchor_spans": [ [ 0, 20 ] ] } ]

[ "Data_transmission", "Telegraphy" ]

[]

[ { "plaintext": "In telecommunication, the term frequency compatibility has the following meanings: ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374 ], "anchor_spans": [ [ 3, 20 ] ] }, { "plaintext": "1. Of an electronic device, the extent to which it will operate at its designed performance level in its intended operational environment (including the presence of interference) without causing interference to other devices. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 2889864 ], "anchor_spans": [ [ 166, 178 ] ] }, { "plaintext": "2. The degree to which an electrical or electronic device or devices operating on or responding to a specified frequency or frequencies is capable of functioning with other such devices.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10779 ], "anchor_spans": [ [ 112, 121 ] ] }, { "plaintext": "electromagnetic compatibility", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 41093 ], "anchor_spans": [ [ 0, 29 ] ] } ]

[ "Electromagnetic_compatibility" ]

[]

[ { "plaintext": "Frequency deviation () is used in FM radio to describe the difference between the minimum or maximum extent of a frequency modulated signal, and the nominal center or carrier frequency. The term is sometimes mistakenly used as synonymous with frequency drift, which is an unintended offset of an oscillator from its nominal frequency.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10835, 153217, 5439832 ], "anchor_spans": [ [ 34, 42 ], [ 167, 184 ], [ 243, 258 ] ] }, { "plaintext": "The frequency deviation of a radio is of particular importance in relation to bandwidth, because less deviation means that more channels can fit into the same amount of frequency spectrum. The FM broadcasting range between 87.5 and 108MHz uses a typical channel spacing of 100 or 200kHz, with a maximum frequency deviation of +/-75kHz, in some cases leaving a buffer above the highest and below the lowest frequency to reduce interaction with other channels.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 3967, 202672, 1607203 ], "anchor_spans": [ [ 78, 87 ], [ 169, 187 ], [ 193, 208 ] ] }, { "plaintext": "The most common FM transmitting applications use peak deviations of +/-75kHz (100 or 200kHz spacing), +/-5kHz (15–25kHz spacing), +/-2.5kHz (3.75-12.5kHz spacing), and +/-2kHz (8.33kHz spacing, 7.5kHz spacing, 6.25kHz spacing or 5kHz spacing).", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Frequency modulation", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 10835 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Carson bandwidth rule", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 40851 ], "anchor_spans": [ [ 1, 22 ] ] } ]

[ "Radio_modulation_modes", "Frequency-domain_analysis" ]

[ "absolute frequency deviation" ]

[ { "plaintext": "In telegraphy, frequency-exchange signaling or two-source frequency keying is frequency-change signaling in which the change from one significant condition to another is accompanied by decay in amplitude of one or more frequencies and by buildup in amplitude of one or more other frequencies.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 30010, 41185, 2518170, 10779 ], "anchor_spans": [ [ 3, 13 ], [ 78, 104 ], [ 134, 155 ], [ 219, 230 ] ] }, { "plaintext": "Frequency-exchange signaling applies to supervisory signaling and user-information transmission. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 2052479, 18985062, 609152 ], "anchor_spans": [ [ 66, 70 ], [ 71, 82 ], [ 83, 95 ] ] }, { "plaintext": "Keying (telecommunications)", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 12481202 ], "anchor_spans": [ [ 0, 27 ] ] } ]

[ "Telegraphy" ]

[]

[ { "plaintext": "In telecommunication, the term frequency frogging has the following meanings: ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374 ], "anchor_spans": [ [ 3, 20 ] ] }, { "plaintext": " The interchanging of the frequencies of carrier channels to accomplish specific purposes, such as to prevent feedback and oscillation, to reduce crosstalk, and to correct for a high frequency response slope in the transmission line. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 153217, 11545, 2995499, 302033, 41811 ], "anchor_spans": [ [ 41, 48 ], [ 110, 118 ], [ 146, 155 ], [ 183, 201 ], [ 215, 232 ] ] }, { "plaintext": " In microwave radio relay systems, the alternate use of two frequencies at repeater sites to prevent feedback and oscillation. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 5540651 ], "anchor_spans": [ [ 4, 25 ] ] }, { "plaintext": "Note: Frequency frogging is accomplished by having modulators, which are integrated into specially designed repeaters, translate a low-frequency group to a high-frequency group, and vice versa. A frequency channel will appear in the low group for one repeater section and will then be translated to the high group for the next section because of frequency frogging. This results in nearly constant attenuation with frequency over two successive repeater sections, and eliminates the need for large slope equalization and adjustments. Singing and crosstalk are minimized because the high-level output of a repeater is at a different frequency than the low-level input to other repeaters. It also diminishes group delay distortion. A repeater that receives on the high band from both direction and sends on the low band is called Hi-Lo; the other kind Lo-Hi.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10779, 20637, 41655, 41222, 4051799, 41655, 40735, 26332696, 41655, 41222 ], "anchor_spans": [ [ 7, 16 ], [ 52, 61 ], [ 109, 117 ], [ 146, 151 ], [ 197, 214 ], [ 252, 260 ], [ 399, 410 ], [ 505, 517 ], [ 606, 614 ], [ 708, 719 ] ] } ]

[ "Communication_circuits" ]

[]

[ { "plaintext": "In telecommunication, frequency sharing or channel sharing is the assignment to or use of the same radio frequency by two or more stations that are separated geographically or that use the frequency at different times. It reduces the potential for mutual interference where the assignment of different frequencies to each user is not practical or possible.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 42852, 1072324, 2052479 ], "anchor_spans": [ [ 3, 20 ], [ 99, 114 ], [ 255, 267 ], [ 322, 326 ] ] }, { "plaintext": "U.S. mobile data usage in 2017 was 40 times that in 2010, forcing frequencies to be reallocated. The FCC's 2016 auction allowed two or more stations to share a single 6MHz television channel while retaining their licenses and all rights.", "section_idx": 1, "section_name": "Channel sharing in digital television", "target_page_ids": [ 39871679 ], "anchor_spans": [ [ 101, 119 ] ] }, { "plaintext": "NBC sold the spectrum of three of its stations in the 2017 FCC auction: WNBC New York, Telemundo WSNS Chicago and WWSI Philadelphia. Other NBC stations in the market would begin channel sharing with those stations;for instance, Comcast moved Channel 28 WNBC onto Telemundo's Channel 35 WNJU, broadcasting both stations from WNJU's antenna. Stations had to either channel-share with another TV station in this way or go off the air by Jan. 23, 2018.", "section_idx": 1, "section_name": "Channel sharing in digital television", "target_page_ids": [ 1196887, 30861540, 1818848 ], "anchor_spans": [ [ 72, 76 ], [ 97, 101 ], [ 114, 118 ] ] } ]

[ "Bandplans" ]

[]

[ { "plaintext": "In the physical sciences and in telecommunication, the term frequency shift may refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Any change in frequency", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10779 ], "anchor_spans": [ [ 15, 24 ] ] }, { "plaintext": " A Doppler shift", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 8724 ], "anchor_spans": [ [ 3, 16 ] ] }, { "plaintext": " In facsimile, a frequency modulation system where one frequency represents picture black and another frequency represents picture white", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10826, 10835 ], "anchor_spans": [ [ 4, 13 ], [ 17, 37 ] ] }, { "plaintext": " Spectrum shifting in signal processing, see Discrete Fourier transform", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 8811 ], "anchor_spans": [ [ 45, 71 ] ] }, { "plaintext": " Frequency mixer", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 482952 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Voice inversion", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 5951995 ], "anchor_spans": [ [ 1, 16 ] ] } ]

[]

[]

[ { "plaintext": "Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier signal. The technology is used for communication systems such as telemetry, weather balloon radiosondes, caller ID, garage door openers, and low frequency radio transmission in the VLF and ELF bands. The simplest FSK is binary FSK (BFSK). BFSK uses a pair of discrete frequencies to transmit binary (0s and 1s) information. With this scheme, the 1 is called the mark frequency and the 0 is called the space frequency.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10835, 153217, 46256, 172851, 162281, 1299689, 160505, 366253, 238686 ], "anchor_spans": [ [ 34, 54 ], [ 146, 160 ], [ 220, 229 ], [ 247, 257 ], [ 260, 269 ], [ 271, 289 ], [ 337, 340 ], [ 345, 348 ], [ 377, 383 ] ] }, { "plaintext": "Reference implementations of FSK modems exist and are documented in detail. The demodulation of a binary FSK signal can be done using the Goertzel algorithm very efficiently, even on low-power microcontrollers.", "section_idx": 1, "section_name": "Modulating and demodulating", "target_page_ids": [ 2133529 ], "anchor_spans": [ [ 138, 156 ] ] }, { "plaintext": "In principle FSK can be implemented by using completely independent free-running oscillators, and switching between them at the beginning of each symbol period.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In general, independent oscillators will not be at the same phase and therefore the same amplitude at the switch-over instant,", "section_idx": 2, "section_name": "Variations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "causing sudden discontinuities in the transmitted signal.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In practice, many FSK transmitters use only a single oscillator, and the process of switching to a different frequency at the beginning of each symbol period preserves the phase.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The elimination of discontinuities in the phase (and therefore elimination of sudden changes in amplitude) reduces sideband power, reducing interference with neighboring channels.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 41701 ], "anchor_spans": [ [ 115, 123 ] ] }, { "plaintext": "Rather than directly modulating the frequency with the digital data symbols, \"instantaneously\" changing the frequency at the beginning of each symbol period, Gaussian frequency-shift keying (GFSK) filters the data pulses with a Gaussian filter to make the transitions smoother. This filter has the advantage of reducing sideband power, reducing interference with neighboring channels, at the cost of increasing intersymbol interference. It is used by Improved Layer 2 Protocol, DECT, Bluetooth, Cypress WirelessUSB, Nordic Semiconductor, Texas Instruments LPRF, IEEE 802.15.4, Z-Wave and Wavenis devices. For basic data rate Bluetooth the minimum deviation is 115kHz.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 5842389, 41701, 41287, 62823244, 8674, 3742, 1084118, 47768, 455777, 2685825, 3742 ], "anchor_spans": [ [ 228, 243 ], [ 320, 328 ], [ 411, 435 ], [ 451, 476 ], [ 478, 482 ], [ 484, 493 ], [ 516, 536 ], [ 538, 555 ], [ 562, 575 ], [ 577, 583 ], [ 625, 634 ] ] }, { "plaintext": "A GFSK modulator differs from a simple frequency-shift keying modulator in that before the baseband waveform (with levels −1 and +1) goes into the FSK modulator, it passed through a Gaussian filter to make the transitions smoother to limit spectral width. Gaussian filtering is a standard way to reduce spectral width; it is called pulse shaping in this application.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 40773, 5842389, 8008408 ], "anchor_spans": [ [ 91, 99 ], [ 182, 197 ], [ 332, 345 ] ] }, { "plaintext": "In ordinary non-filtered FSK, at a jump from −1 to +1 or +1 to −1, the modulated waveform changes rapidly, which introduces large out-of-band spectrum. If the pulse is changed going from −1 to +1 as −1, −0.98, −0.93, ..., +0.93, +0.98, +1, and this smoother pulse is used to determine the carrier frequency, the out-of-band spectrum will be reduced.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 153217 ], "anchor_spans": [ [ 289, 306 ] ] }, { "plaintext": "Minimum frequency-shift keying or minimum-shift keying (MSK) is a particular spectrally efficient form of coherent FSK. In MSK, the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms that represent a 0 and a 1 bit differ by exactly half a carrier period. The maximum frequency deviation is δ=0.25fm, where fm is the maximum modulating frequency. As a result, the modulation index m is 0.5. This is the smallest FSK modulation index that can be chosen such that the waveforms for 0 and 1 are orthogonal.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 41187, 1131440, 102221 ], "anchor_spans": [ [ 329, 348 ], [ 478, 494 ], [ 554, 564 ] ] }, { "plaintext": "A variant of MSK called Gaussian minimum-shift keying (GMSK) is used in the GSM mobile phone standard.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 2261515, 12808, 19644137 ], "anchor_spans": [ [ 55, 59 ], [ 76, 79 ], [ 80, 92 ] ] }, { "plaintext": "Audio frequency-shift keying (AFSK) is a modulation technique by which digital data is represented by changes in the frequency (pitch) of an audio tone, yielding an encoded signal suitable for transmission via radio or telephone. Normally, the transmitted audio alternates between two tones: one, the \"mark\", represents a binary one; the other, the \"space\", represents a binary zero.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 20637, 8276, 10779, 77933, 18994087, 15368428, 30003, 238686 ], "anchor_spans": [ [ 41, 51 ], [ 71, 83 ], [ 117, 126 ], [ 128, 133 ], [ 141, 146 ], [ 210, 215 ], [ 219, 228 ], [ 323, 329 ] ] }, { "plaintext": "AFSK differs from regular frequency-shift keying in performing the modulation at baseband frequencies. In radio applications, the AFSK-modulated signal normally is being used to modulate an RF carrier (using a conventional technique, such as AM or FM) for transmission.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 40773, 42852, 153217, 1140, 10835 ], "anchor_spans": [ [ 81, 89 ], [ 191, 193 ], [ 194, 201 ], [ 243, 245 ], [ 249, 251 ] ] }, { "plaintext": "AFSK is not always used for high-speed data communications, since it is far less efficient in both power and bandwidth than most other modulation modes. In addition to its simplicity, however, AFSK has the advantage that encoded signals will pass through AC-coupled links, including most equipment originally designed to carry music or speech.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 40843 ], "anchor_spans": [ [ 256, 266 ] ] }, { "plaintext": "AFSK is used in the U.S.-based Emergency Alert System to notify stations of the type of emergency, locations affected, and the time of issue without actually hearing the text of the alert.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 175507 ], "anchor_spans": [ [ 31, 53 ] ] }, { "plaintext": "Phase 1 radios in the Project 25 system use continuous 4-level FM (C4FM) modulation.", "section_idx": 2, "section_name": "Variations", "target_page_ids": [ 1041955 ], "anchor_spans": [ [ 22, 32 ] ] }, { "plaintext": "In 1910, Reginald Fessenden invented a two-tone method of transmitting Morse code. Dots and dashes were replaced with different tones of equal length. The intent was to minimize transmission time.", "section_idx": 3, "section_name": "Applications", "target_page_ids": [ 96883 ], "anchor_spans": [ [ 9, 27 ] ] }, { "plaintext": "Some early CW transmitters employed an arc converter that could not be conveniently keyed. Instead of turning the arc on and off, the key slightly changed the transmitter frequency in a technique known as the compensation-wave method. The compensation-wave was not used at the receiver. Spark transmitters used for this method consumed a lot of bandwidth and caused interference, so it was discouraged by 1921.", "section_idx": 3, "section_name": "Applications", "target_page_ids": [ 4196082, 1408014, 1105907 ], "anchor_spans": [ [ 39, 52 ], [ 84, 89 ], [ 287, 305 ] ] }, { "plaintext": "Most early telephone-line modems used audio frequency-shift keying (AFSK) to send and receive data at rates up to about 1200bits per second. The Bell 103 and Bell 202 modems used this technique. Even today, North American caller ID uses 1200baud AFSK in the form of the Bell 202 standard. Some early microcomputers used a specific form of AFSK modulation, the Kansas City standard, to store data on audio cassettes. AFSK is still widely used in amateur radio, as it allows data transmission through unmodified voiceband equipment.", "section_idx": 3, "section_name": "Applications", "target_page_ids": [ 20647197, 1407798, 1414302, 162281, 1414302, 48144, 194388, 65880, 23275402 ], "anchor_spans": [ [ 26, 31 ], [ 145, 153 ], [ 158, 166 ], [ 222, 231 ], [ 270, 278 ], [ 300, 313 ], [ 360, 380 ], [ 399, 413 ], [ 445, 458 ] ] }, { "plaintext": "AFSK is also used in the United States' Emergency Alert System to transmit warning information. It is used at higher bitrates for Weathercopy used on Weatheradio by NOAA in the U.S.", "section_idx": 3, "section_name": "Applications", "target_page_ids": [ 175507, 272290, 3574810, 37876 ], "anchor_spans": [ [ 40, 62 ], [ 117, 124 ], [ 150, 161 ], [ 165, 169 ] ] }, { "plaintext": "The CHU shortwave radio station in Ottawa, Ontario, Canada broadcasts an exclusive digital time signal encoded using AFSK modulation.", "section_idx": 3, "section_name": "Applications", "target_page_ids": [ 285856, 57980, 22219 ], "anchor_spans": [ [ 4, 7 ], [ 8, 23 ], [ 35, 50 ] ] }, { "plaintext": "Frequency-shift keying (FSK) is commonly used over telephone lines for caller ID (displaying callers' numbers) and remote metering applications. There are several variations of this technology.", "section_idx": 4, "section_name": "Caller ID and remote metering standards", "target_page_ids": [ 162281, 435397 ], "anchor_spans": [ [ 71, 80 ], [ 115, 130 ] ] }, { "plaintext": "In some countries of Europe, the European Telecommunications Standards Institute (ETSI) standards 200 778-1 and -2 replacing 300 778-1 & -2 allow 3 physical transport layers (Telcordia Technologies (formerly Bellcore), British Telecom (BT) and Cable Communications Association (CCA)), combined with 2 data formats Multiple Data Message Format (MDMF) & Single Data Message Format (SDMF), plus the Dual-tone multi-frequency (DTMF) system and a no-ring mode for meter-reading and the like. It's more of a recognition that the different types exist than an attempt to define a single \"standard\".", "section_idx": 4, "section_name": "Caller ID and remote metering standards", "target_page_ids": [ 9239, 18934452, 1141972, 4642, 162281, 162281, 8488 ], "anchor_spans": [ [ 21, 27 ], [ 33, 80 ], [ 177, 199 ], [ 221, 236 ], [ 316, 344 ], [ 354, 380 ], [ 398, 423 ] ] }, { "plaintext": "The Telcordia Technologies (formerly Bellcore) standard is used in the United States, Canada (but see below), Australia, China, Hong Kong and Singapore. It sends the data after the first ring tone and uses the 1200 bits per second Bell 202 tone modulation. The data may be sent in SDMF which includes the date, time and number or in MDMF, which adds a NAME field.", "section_idx": 4, "section_name": "Caller ID and remote metering standards", "target_page_ids": [ 1141972, 3434750, 4689264, 5405, 13404, 27318, 272290, 1414302 ], "anchor_spans": [ [ 4, 26 ], [ 71, 84 ], [ 110, 119 ], [ 121, 126 ], [ 128, 137 ], [ 142, 151 ], [ 215, 230 ], [ 231, 239 ] ] }, { "plaintext": "British Telecom (BT) in the United Kingdom developed their own standard, which wakes up the display with a line reversal, then sends the data as CCITT v.23 modem tones in a format similar to MDMF. It is used by BT, wireless networks like the late Ionica, and some cable companies. Details are to be found in BT Supplier Information Notes (SINs) 227(link broken 28/7/21) and 242(link broken 28/7/21); another useful document is Designing Caller Identification Delivery Using XR-2211 for BT from the EXAR website.", "section_idx": 4, "section_name": "Caller ID and remote metering standards", "target_page_ids": [ 4642, 31717, 14744, 1759007 ], "anchor_spans": [ [ 0, 15 ], [ 28, 42 ], [ 145, 150 ], [ 247, 253 ] ] }, { "plaintext": "The Cable Communications Association (CCA) of the United Kingdom developed their own standard which sends the information after a short first ring, as either Bell 202 or V.23 tones. They developed a new standard rather than change some \"street boxes\" (multiplexors) which couldn't cope with the BT standard. The UK cable industry use a variety of switches: most are Nortel DMS-100; some are System X; System Y; and Nokia DX220. Note that some of these use the BT standard instead of the CCA one. The data format is similar to the BT one, but the transport layer is more like Telcordia Technologies, so North American or European equipment is more likely to detect it.", "section_idx": 4, "section_name": "Caller ID and remote metering standards", "target_page_ids": [ 1414302, 1340477, 21243, 991365, 2519868, 21242, 21139 ], "anchor_spans": [ [ 158, 166 ], [ 170, 174 ], [ 366, 372 ], [ 391, 399 ], [ 401, 409 ], [ 415, 420 ], [ 602, 615 ] ] }, { "plaintext": " Amplitude-shift keying (ASK)", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 946426 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Continuous-phase frequency-shift keying (CPFSK)", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 905348 ], "anchor_spans": [ [ 1, 40 ] ] }, { "plaintext": " Dual-tone multi-frequency (DTMF), another encoding technique representing data by pairs of audio frequencies", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 8488 ], "anchor_spans": [ [ 1, 26 ] ] }, { "plaintext": " Frequency-change signaling", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 41185 ], "anchor_spans": [ [ 1, 27 ] ] }, { "plaintext": " Multiple frequency-shift keying (MFSK)", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 2371591 ], "anchor_spans": [ [ 1, 32 ] ] }, { "plaintext": " Orthogonal frequency-division multiplexing (OFDM)", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 22691 ], "anchor_spans": [ [ 1, 43 ] ] }, { "plaintext": " Phase-shift keying (PSK)", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 41551 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Federal Standard 1037C", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 37310 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " MIL-STD-188", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 41882 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Spread frequency-shift keying (S-FSK)", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 23491906 ], "anchor_spans": [ [ 1, 30 ] ] }, { "plaintext": " . Revised to April 24, 1921.", "section_idx": 6, "section_name": "References", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "dFSK: Distributed Frequency Shift Keying Modulation in Dense Sensor Networks", "section_idx": 7, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " M Nasseri, J Kim, M Alam - Proceedings of the 17th Communications & Networking, 2014, Unified metric calculation of sampling-based turbo-coded noncoherent MFSK for mobile channel", "section_idx": 7, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " J Kim, P Raorane, M Nasseri, M Alam - Proceedings of the 46th Annual Simulation Symposium, 2013, Performance analysis of sampling-based turbo coded NCQFSK for image data transmission", "section_idx": 7, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Amateur_radio", "Caller_ID", "Quantized_radio_modulation_modes" ]

[ "FSK" ]

[ { "plaintext": "A frequency standard is a stable oscillator used for frequency calibration or reference. A frequency standard generates a fundamental frequency with a high degree of accuracy and precision. Harmonics of this fundamental frequency are used to provide reference points.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 9920, 10779, 47502, 11490, 41932 ], "anchor_spans": [ [ 33, 43 ], [ 53, 62 ], [ 63, 74 ], [ 122, 143 ], [ 166, 188 ] ] }, { "plaintext": "Since time is the reciprocal of frequency, it is relatively easy to derive a time standard from a frequency standard. A standard clock comprises a frequency standard, a device to count off the cycles of the oscillation emitted by the frequency standard, and a means of displaying or outputting the result.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41799 ], "anchor_spans": [ [ 77, 90 ] ] }, { "plaintext": "Frequency standards in a network or facility are sometimes administratively designated as primary or secondary. The terms primary and secondary, as used in this context, should not be confused with the respective technical meanings of these words in the discipline of precise time and frequency.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 46545, 41132 ], "anchor_spans": [ [ 25, 32 ], [ 36, 44 ] ] }, { "plaintext": "A frequency reference is an instrument used for providing a stable frequency of some kind. There are different sorts of frequency references, acoustic ones such as tuning forks but also electrical ones that emit a signal of a certain frequency (a frequency standard).", "section_idx": 1, "section_name": "Frequency reference", "target_page_ids": [ 1198, 31198 ], "anchor_spans": [ [ 142, 150 ], [ 164, 175 ] ] }, { "plaintext": "Among the most stable frequency references in the world are cesium standards (including cesium fountains) and hydrogen masers. Cesium standards are widely recognized as having better long-term stability, whereas hydrogen masers can attain superior short-term performance; therefore, several national standards laboratories use ensembles of cesium standards and hydrogen masers in order to combine the best attributes of both.", "section_idx": 1, "section_name": "Frequency reference", "target_page_ids": [ 40858, 16899513, 16836458, 65637 ], "anchor_spans": [ [ 60, 75 ], [ 88, 103 ], [ 110, 124 ], [ 300, 322 ] ] }, { "plaintext": "The carrier of time signal transmitters, Loran-C transmitters and of several long wave and medium wave broadcasting stations is derived from an atomic clock and can be therefore used as frequency standard.", "section_idx": 1, "section_name": "Frequency reference", "target_page_ids": [ 182679, 18376, 168741, 110381 ], "anchor_spans": [ [ 15, 26 ], [ 41, 48 ], [ 77, 86 ], [ 91, 102 ] ] }, { "plaintext": " Rubidium standard", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 41674 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Atomic clock", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 25453985 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Standard frequency and time signal service", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 48760973 ], "anchor_spans": [ [ 1, 43 ] ] } ]

[ "Electronics_standards", "Frequency" ]

[]

[ { "plaintext": "A Fresnel zone ( ), named after physicist Augustin-Jean Fresnel, is one of a series of confocal prolate ellipsoidal regions of space between and around a transmitter and a receiver. The primary wave will travel in a relative straight line from the transmitter to the receiver. Aberrant transmitted radio, sound, or light waves which are transmitted at the same time can follow slightly different paths before reaching a receiver, especially if there are obstructions or deflecting objects between the two. The two waves can arrive at the receiver at slightly different times and the aberrant wave may arrive out of phase with the primary wave due to the different path lengths. Depending on the magnitude of the phase difference between the two waves, the waves can interfere constructively or destructively. The size of the calculated Fresnel zone at any particular distance from the transmitter and receiver can help to predict whether obstructions or discontinuities along the path will cause significant interference.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 1141, 82365, 145381, 41385, 15112 ], "anchor_spans": [ [ 42, 63 ], [ 96, 103 ], [ 104, 113 ], [ 370, 432 ], [ 757, 812 ] ] }, { "plaintext": "In any wave-propagated transmission between a transmitter and receiver, some amount of the radiated wave propagates off-axis (not on the line-of-sight path between transmitter and receiver). This can then deflect off objects and then radiate to the receiver. However, the direct-path wave and the deflected-path wave may arrive out of phase, leading to destructive interference when the phase difference is half an odd integer () multiple of the period. The n-th Fresnel zone is defined as the locus of points in 3D space such that a 2-segment path from the transmitter to the receiver that deflects off a point on that surface will be between n-1 and n half-wavelengths out of phase with the straight-line path. The boundaries of these zones will be ellipsoids with foci at the transmitter and receiver. In order to ensure limited interference, such transmission paths are designed with a certain clearance distance determined by a Fresnel-zone analysis. ", "section_idx": 1, "section_name": "Significance", "target_page_ids": [ 521267, 24047, 15112, 10779 ], "anchor_spans": [ [ 205, 212 ], [ 335, 340 ], [ 353, 377 ], [ 446, 452 ] ] }, { "plaintext": "The dependence on the interference on clearance is the cause of the picket-fencing effect when either the radio transmitter or receiver is moving, and the high and low signal strength zones are above and below the receiver's cut-off threshold. The extreme variations of signal strength at the receiver can cause interruptions in the communications link, or even prevent a signal from being received at all.", "section_idx": 1, "section_name": "Significance", "target_page_ids": [ 9488727 ], "anchor_spans": [ [ 225, 242 ] ] }, { "plaintext": "Fresnel zones are seen in optics, radio communications, electrodynamics, seismology, acoustics, gravitational radiation, and other situations involving the radiation of waves and multipath propagation. Fresnel zone computations are used to anticipate obstacle clearances required when designing highly directive systems such as microwave parabolic antenna systems. Although intuitively, clear line-of-sight between transmitter and receiver may seem to be all that is required for a strong antenna system, but because of the complex nature of radio waves, obstructions within the first Fresnel zone can cause significant weakness, even if those obstructions are not blocking the apparent line-of-sight signal path. For this reason, it is valuable to do a calculation of the size of the 1st, or primary, Fresnel zone for a given antenna system. Doing this will enable the antenna installer to decide if an obstacle, such as a tree, is going to make a significant impact on signal strength. The rule of thumb is that the primary Fresnel zone would ideally be 80% clear of obstacles, but must be at least 60% clear.", "section_idx": 1, "section_name": "Significance", "target_page_ids": [ 22483, 15368428, 9532, 3764047, 1198, 8111079, 41385, 5540651, 208264 ], "anchor_spans": [ [ 26, 32 ], [ 34, 54 ], [ 56, 71 ], [ 73, 83 ], [ 85, 94 ], [ 96, 119 ], [ 179, 200 ], [ 328, 337 ], [ 338, 355 ] ] }, { "plaintext": "Fresnel zones are confocal prolate ellipsoidal shaped regions in space (e.g. 1, 2, 3), centered around the line of the direct transmission path (path AB on the diagram). The first region includes the ellipsoidal space which the direct line-of-sight signal passes through. If a stray component of the transmitted signal bounces off an object within this region and then arrives at the receiving antenna, the phase shift will be something less than a quarter-length wave, or less than a 90º shift (path ACB on the diagram). The effect regarding phase-shift alone will be minimal. Therefore, this bounced signal can potentially result in having a positive impact on the receiver, as it is receiving a stronger signal than it would have without the deflection, and the additional signal will potentially be mostly in-phase. However, the positive attributes of this deflection also depends on the polarization of the signal relative to the object (see the section on polarization under the Talk tab). ", "section_idx": 2, "section_name": "Spatial structure", "target_page_ids": [ 82365, 145381, 24047 ], "anchor_spans": [ [ 27, 34 ], [ 35, 44 ], [ 407, 418 ] ] }, { "plaintext": "The 2nd region surrounds the 1st region but excludes it. If a reflective object is located in the 2nd region, the stray sine-wave which has bounced from this object and has been captured by the receiver will be shifted more than 90º but less than 270º because of the increased path length, and will potentially be received out-of-phase. Generally this is unfavorable. But again, this depends on polarization (see the section on polarization under the Talk tab). Use of same circular polarization (e.g. right) in both ends, will eliminate odd number of reflections (including one).", "section_idx": 2, "section_name": "Spatial structure", "target_page_ids": [ 40875 ], "anchor_spans": [ [ 474, 495 ] ] }, { "plaintext": "The 3rd region surrounds the 2nd region and deflected waves captured by the receiver will have the same effect as a wave in the 1st region. That is, the sine wave will have shifted more than 270º but less than 450º (ideally it would be a 360º shift) and will therefore arrive at the receiver with the same shift as a signal might arrive from the 1st region. A wave deflected from this region has the potential to be shifted precisely one wavelength so that it is exactly in sync with the line-of-sight wave when it arrives at the receiving antenna.", "section_idx": 2, "section_name": "Spatial structure", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The 4th region surrounds the 3rd region and is similar to the 2nd region. And so on. ", "section_idx": 2, "section_name": "Spatial structure", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "If unobstructed and in a perfect environment, radio waves will travel in a relatively straight line from the transmitter to the receiver. But if there are reflective surfaces that interact with a stray transmitted wave, such as bodies of water, smooth terrain, roof tops, sides of buildings, etc., the radio waves deflecting off those surfaces may arrive either out-of-phase or in-phase with the signals that travel directly to the receiver. Sometimes this results in the counter-intuitive finding that reducing the height of an antenna increases the signal-to-noise ratio at the receiver. ", "section_idx": 2, "section_name": "Spatial structure", "target_page_ids": [ 41706 ], "anchor_spans": [ [ 551, 572 ] ] }, { "plaintext": "Although radio waves generally travel in a relative straight line, fog and even humidity can cause some of the signal in certain frequencies to scatter or bend before reaching the receiver. This means objects which are clear of the line of sight path will still potentially block parts of the signal. To maximize signal strength, one needs to minimize the effect of obstruction loss by removing obstacles from both the direct radio frequency line of sight (RF LoS) line and also the area around it within the primary Fresnel zone. The strongest signals are on the direct line between transmitter and receiver and always lie in the first Fresnel zone.", "section_idx": 2, "section_name": "Spatial structure", "target_page_ids": [ 60455 ], "anchor_spans": [ [ 442, 455 ] ] }, { "plaintext": "In the early 19th century, French scientist Augustin-Jean Fresnel created a method to calculate where the zones are — that is, whether a given obstacle will cause mostly in-phase or mostly out-of-phase deflections between the transmitter and the receiver.", "section_idx": 2, "section_name": "Spatial structure", "target_page_ids": [ 1141 ], "anchor_spans": [ [ 44, 65 ] ] }, { "plaintext": "The concept of Fresnel zone clearance may be used to analyze interference by obstacles near the path of a radio beam. The first zone must be kept largely free from obstructions to avoid interfering with the radio reception. However, some obstruction of the Fresnel zones can often be tolerated. As a rule of thumb the maximum obstruction allowable is 40%, but the recommended obstruction is 20% or less.", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [ 2889864, 56538 ], "anchor_spans": [ [ 61, 73 ], [ 300, 313 ] ] }, { "plaintext": "For establishing Fresnel zones, first determine the RF line of sight (RF LoS), which in simple terms is a straight line between the transmitting and receiving antennas. Now the zone surrounding the RF LoS is said to be the Fresnel zone.", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The cross sectional radius of each Fresnel zone is the longest at the midpoint of the RF LoS, shrinking to a point at each vertex, behind the antennas.", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Consider an arbitrary point P in the LoS, at a distance and with respect to each of the two antennas.", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "To obtain the radius of zone , note that the volume of the zone is delimited by all points for which the difference in distances, between the direct wave () and the reflected wave () is the constant (multiples of half a wavelength). This effectively defines an ellipsoid with the major axis along and foci at the antennas (points A and B). So:", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [ 33125 ], "anchor_spans": [ [ 222, 232 ] ] }, { "plaintext": "Re-writing the expression with the coordinates of point and the distance between antennas , it gives:", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Assuming the distances between the antennas and the point are much larger than the radius and applying the binomial approximation for the square root, (for x≪1), the expression simplifies to:", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [ 11376019 ], "anchor_spans": [ [ 108, 130 ] ] }, { "plaintext": "which can be solved for :", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For a satellite-to-Earth link, it further simplifies to:", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Note that when or , which implies that the foci seem to coincide with the vertices of the ellipsoid. This is not correct and it's a consequence of the approximation made. ", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [ 6865890 ], "anchor_spans": [ [ 75, 83 ] ] }, { "plaintext": "Setting the point to one of the vertices (behind an antenna), it's possible to obtain the error of this approximation:", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Since the distance between antennas is generally tens of km and of the order of cm, the error is negligible for a graphical representation.", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "On the other hand, considering the clearance at the left-hand antenna, with , and applying the binomial approximation only at the right-hand antenna, we find:", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The quadratic polynomial roots are:", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Applying the binomial approximation one last time, we finally find:", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "So, there should be at least half a wavelength of clearance at the antenna in the direction perpendicular to the line of sight.", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The vertical clearance at the antenna in a slant direction inclined at an altitude angle a would be:", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [ 41720, 48386 ], "anchor_spans": [ [ 43, 58 ], [ 74, 88 ] ] }, { "plaintext": "For practical applications, it is often useful to know the maximum radius of the first Fresnel zone. Using , , and in the above formula gives", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the distance between the two antennas,", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the frequency of the transmitted signal,", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [ 10779 ], "anchor_spans": [ [ 8, 17 ] ] }, { "plaintext": " ≈ is the speed of light in the air.", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [ 28736 ], "anchor_spans": [ [ 11, 25 ] ] }, { "plaintext": "Substitution of the numeric value for followed by a unit conversion results in an easy way to calculate the radius of the first Fresnel zone , knowing the distance between the two antennas and the frequency of the transmitted signal :", "section_idx": 3, "section_name": "Clearance calculation", "target_page_ids": [ 5390 ], "anchor_spans": [ [ 53, 68 ] ] }, { "plaintext": " Beam diameter", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 40780 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Diversity scheme", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 7397903 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Ellipse", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 9277 ], "anchor_spans": [ [ 1, 8 ] ] }, { "plaintext": " Fresnel diffraction", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 2649192 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": " Fresnel integral", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 271143 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Fresnel number", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 2938800 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Fresnel zone plate", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 901172 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Fresnel zone antenna", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 31712770 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Microwave", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 20097 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " Near field", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 271708 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Path loss", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 41492 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " Rain fade", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 767065 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " Weissberger's model", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 5589647 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": "Online Fresnel Zone Calculator: Support the global language", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Generate 3D Fresnel zone, as a Google Earth KML file", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Fresnel zone calculator and elevation chart", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Fresnel zone calculator", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "FEN Fresnel zone calculator", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "More Fresnel zone details", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "R.E. Sherriff, Understanding the Fresnel zone", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "VHF/UHF/Microwave Radio Propagation: A Primer for Digital Experimenters", "section_idx": 6, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Diffraction", "Radio_frequency_propagation" ]

[]

[ { "plaintext": "In telecommunication, the term front-to-back ratio (also known as front-to-rear ratio) can mean:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The ratio of power gain between the front and rear of a directional antenna. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 342371 ], "anchor_spans": [ [ 56, 75 ] ] }, { "plaintext": "Ratio of signal strength transmitted in a forward direction to that transmitted in a backward direction. For receiving antennas, the ratio of received-signal strength when the antenna is rotated 180°.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 690346 ], "anchor_spans": [ [ 9, 24 ] ] }, { "plaintext": "The ratio compares the antenna gain in a specified direction, i.e., azimuth, usually that of maximum gain, to the gain in a direction 180° from the specified azimuth. A front-to-back ratio is usually expressed in dB. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 49693, 47487, 8410 ], "anchor_spans": [ [ 23, 35 ], [ 68, 75 ], [ 213, 215 ] ] }, { "plaintext": "In point-to-point microwave antennas, a \"high performance\" antenna usually has a higher front to back ratio than other antennas. For example, an unshrouded 38 GHz microwave dish may have a front to back ratio of 64 dB, while the same size reflector equipped with a shroud would have a front to back ratio of 70 dB. Other factors affecting the front to back ratio of a parabolic microwave antenna include the material of the dish and the precision with which the reflector itself was formed.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 13214323 ], "anchor_spans": [ [ 3, 17 ] ] }, { "plaintext": "In other electrical engineering the front to back ratio is a ratio of parameters used to characterize rectifiers or other devices, in which electric current, signal strength, resistance, or other parameters, in one direction is compared with that in the opposite direction.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 87837, 60569, 6207, 61577 ], "anchor_spans": [ [ 61, 66 ], [ 102, 111 ], [ 140, 156 ], [ 175, 185 ] ] } ]

[ "Antennas", "Engineering_ratios" ]

[]

[ { "plaintext": "Federal Telecommunications System 2000 (FTS2000) is a long distance telecommunications service for the United States federal government, including services such as switched voice service for voice or data up to 4.8 kbit/s, switched data at 56 kbit/s and 64 kbit/s, switched digital integrated service for voice, data, image, and video up to 1.544 Mbit/s, packet switched service for data in packet form, video transmission for both compressed and wideband video, and dedicated point-to-point private line for voice and data. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41782, 18985040, 8276, 32441, 43734, 609152, 863794, 41584 ], "anchor_spans": [ [ 68, 94 ], [ 200, 204 ], [ 274, 281 ], [ 329, 334 ], [ 355, 361 ], [ 410, 422 ], [ 447, 455 ], [ 492, 504 ] ] }, { "plaintext": "Note 1: Use of FTS2000 contract services is mandatory for use by U.S. Government agencies for all acquisitions subject to 40 U.S.C. 759. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Note 2: No U.S. Government information processing equipment or customer premises equipment other than that which are required to provide an FTS2000 service are furnished. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 18985062, 40982 ], "anchor_spans": [ [ 28, 39 ], [ 64, 91 ] ] }, { "plaintext": "Note 3: The FTS2000 contractors will be required to provide service directly to an agency's terminal equipment interface. For example, the FTS2000 contractor might provide a terminal adapter to an agency location in order to connect FTS2000 ISDN services to the agency's terminal equipment. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41786, 41409, 41785, 15231 ], "anchor_spans": [ [ 93, 111 ], [ 112, 121 ], [ 175, 191 ], [ 242, 246 ] ] }, { "plaintext": "Note 4: GSA awarded two 10-year, fixed-price contracts covering FTS2000 services on December 7, 1988. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Note 5: The Warner Amendment excludes the mandatory use of FTS2000 in instances related to maximum security.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41684 ], "anchor_spans": [ [ 100, 108 ] ] }, { "plaintext": "FTS2000 was completed in 2000, then replaced by FTS2001, and thereafter, in 2008, by Networx.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 9917684 ], "anchor_spans": [ [ 85, 92 ] ] }, { "plaintext": "FTS2000 was completed in 2000, and was replaced by FTS2001.", "section_idx": 1, "section_name": "References", "target_page_ids": [], "anchor_spans": [] } ]

[ "Telecommunication_services", "Telecommunications_in_the_United_States" ]

[]

[ { "plaintext": "In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum amplitude.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 437701 ], "anchor_spans": [ [ 101, 121 ] ] }, { "plaintext": "Half width at half maximum (HWHM) is half of the FWHM if the function is symmetric.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The term full duration at half maximum (FDHM) is preferred when the independent variable is time.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 30012 ], "anchor_spans": [ [ 92, 96 ] ] }, { "plaintext": "FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of spectrometers.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 527784, 41729, 33094374, 45311025 ], "anchor_spans": [ [ 53, 58 ], [ 77, 91 ], [ 120, 134 ], [ 157, 169 ] ] }, { "plaintext": "The convention of \"width\" meaning \"half maximum\" is also widely used in signal processing to define bandwidth as \"width of frequency range where less than half the signal's power is attenuated\", i.e., the power is at least half the maximum. In signal processing terms, this is at most −3dB of attenuation, called half-power point or, more specifically, half-power bandwidth.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 29324, 3967, 8410, 4020102 ], "anchor_spans": [ [ 72, 89 ], [ 100, 109 ], [ 287, 289 ], [ 353, 373 ] ] }, { "plaintext": "When half-power point is applied to antenna beam width, it is called half-power beam width.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 40780, 40780 ], "anchor_spans": [ [ 44, 54 ], [ 69, 90 ] ] }, { "plaintext": "If the considered function is the density of a normal distribution of the form", "section_idx": 1, "section_name": "Specific distributions", "target_page_ids": [ 21462 ], "anchor_spans": [ [ 47, 66 ] ] }, { "plaintext": "where σ is the standard deviation and x0 is the expected value, then the relationship between FWHM and the standard deviation is", "section_idx": 1, "section_name": "Specific distributions", "target_page_ids": [ 27590, 9653, 27590 ], "anchor_spans": [ [ 15, 33 ], [ 48, 62 ], [ 107, 125 ] ] }, { "plaintext": "The corresponding area within this FWHM accounts to approximately 76%.", "section_idx": 1, "section_name": "Specific distributions", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The width does not depend on the expected value x0; it is invariant under translations.", "section_idx": 1, "section_name": "Specific distributions", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "If the FWHM of a Gaussian function is known, then it can be integrated by simple multiplication.", "section_idx": 1, "section_name": "Specific distributions", "target_page_ids": [ 245552 ], "anchor_spans": [ [ 17, 34 ] ] }, { "plaintext": "In spectroscopy half the width at half maximum (here γ), HWHM, is in common use. For example, a Lorentzian/Cauchy distribution of height can be defined by", "section_idx": 1, "section_name": "Specific distributions", "target_page_ids": [ 27752, 7003 ], "anchor_spans": [ [ 3, 15 ], [ 96, 126 ] ] }, { "plaintext": "Another important distribution function, related to solitons in optics, is the hyperbolic secant:", "section_idx": 1, "section_name": "Specific distributions", "target_page_ids": [ 51654, 22483, 2026043 ], "anchor_spans": [ [ 52, 59 ], [ 64, 70 ], [ 79, 96 ] ] }, { "plaintext": "Any translating element was omitted, since it does not affect the FWHM. For this impulse we have:", "section_idx": 1, "section_name": "Specific distributions", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where is the inverse hyperbolic secant.", "section_idx": 1, "section_name": "Specific distributions", "target_page_ids": [ 3804557 ], "anchor_spans": [ [ 14, 39 ] ] }, { "plaintext": "Gaussian function", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 245552 ], "anchor_spans": [ [ 0, 17 ] ] }, { "plaintext": "Cutoff frequency", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 40986 ], "anchor_spans": [ [ 0, 16 ] ] }, { "plaintext": "FWHM at Wolfram Mathworld", "section_idx": 4, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Statistical_deviation_and_dispersion", "Telecommunication_theory", "Waves" ]

[ "FWHM" ]

[ { "plaintext": "In telecommunication, a functional profile is a standardization document that characterizes the requirements of a standard or group of standards, and specifies how the options and ambiguities in the standard(s) should be interpreted or implemented to (a) provide a particular information technology function, (b) provide for the development of uniform, recognized tests, and (c) promote interoperability among different network elements and terminal equipment that implement a specific profile.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 27065, 18985062, 41285, 46545, 41786 ], "anchor_spans": [ [ 3, 20 ], [ 114, 122 ], [ 276, 287 ], [ 387, 403 ], [ 420, 427 ], [ 441, 459 ] ] } ]

[ "Telecommunications_standards" ]

[]

[ { "plaintext": "Fuse or FUSE may refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Fuse (electrical), a device used in electrical systems to protect against excessive current", "section_idx": 1, "section_name": "Devices", "target_page_ids": [ 683342 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Fuse (automotive), a class of fuses for vehicles", "section_idx": 1, "section_name": "Devices", "target_page_ids": [ 24098303 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Fuse (hydraulic), a device used in hydraulic systems to protect against sudden loss of fluid pressure", "section_idx": 1, "section_name": "Devices", "target_page_ids": [ 2377391 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Fuse (explosives) or fuze, the part of the device that initiates function", "section_idx": 1, "section_name": "Devices", "target_page_ids": [ 683343 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Fuze or fuse, a mechanism for exploding military munitions such as bombs, shells, and mines", "section_idx": 1, "section_name": "Devices", "target_page_ids": [ 19881804 ], "anchor_spans": [ [ 1, 5 ] ] }, { "plaintext": " Fuse ESB, an open-source integration platform based on Apache Camel", "section_idx": 2, "section_name": "Computing", "target_page_ids": [ 16766669 ], "anchor_spans": [ [ 1, 9 ] ] }, { "plaintext": " Filesystem in Userspace, a virtual file system interface for Unix-like operating systems", "section_idx": 2, "section_name": "Computing", "target_page_ids": [ 1219082 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Fuse (emulator), the Free Unix Spectrum Emulator of the ZX Spectrum", "section_idx": 2, "section_name": "Computing", "target_page_ids": [ 8710942 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Fuse Internet Service, a former Cincinnati Bell Internet service provider based in Cincinnati, Ohio, United States", "section_idx": 2, "section_name": "Computing", "target_page_ids": [ 862622 ], "anchor_spans": [ [ 33, 48 ] ] }, { "plaintext": " Fuse Universal, a learning platform", "section_idx": 2, "section_name": "Computing", "target_page_ids": [ 41638811 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Far Ultraviolet Spectroscopic Explorer, a space-based ultraviolet telescope and spectroscope", "section_idx": 3, "section_name": "Science", "target_page_ids": [ 939966 ], "anchor_spans": [ [ 1, 39 ] ] }, { "plaintext": " Intramembranous ossification, the fusing of bones of the skeletal system", "section_idx": 3, "section_name": "Science", "target_page_ids": [ 1311539 ], "anchor_spans": [ [ 1, 29 ] ] }, { "plaintext": " Cell fusion, several biological cells combining", "section_idx": 3, "section_name": "Science", "target_page_ids": [ 12240016 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Fuse (thermonuclear)", "section_idx": 3, "section_name": "Science", "target_page_ids": [ 21544 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Fused compound, a class of multi-ring chemical structures", "section_idx": 3, "section_name": "Science", "target_page_ids": [ 1252834 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Fuse (film), a 2003 film by Pjer Žalica, original Bosnian title Gori vatra", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 29214367 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Fuse Teppō Musume no Torimonochō, a 2012 Japanese animated film", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 36523120 ], "anchor_spans": [ [ 1, 33 ] ] }, { "plaintext": " Fuse (magazine), a Canadian arts and culture magazine", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 31973244 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Fuse (band)", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 18418642 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Fuse (Fuse album), a 1970 album by the above band", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 522961 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " The Fuse (Scottish band), a band from the East of Scotland", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 19050813 ], "anchor_spans": [ [ 1, 25 ] ] }, { "plaintext": " Fuse (Joe Henry album), a 1999 album by Joe Henry", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 523022 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Fuse (Colin James album), a 2000 album by Colin James", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 446347 ], "anchor_spans": [ [ 1, 25 ] ] }, { "plaintext": " Fuse (Keith Urban album), a 2013 album by Keith Urban", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 40190006 ], "anchor_spans": [ [ 1, 25 ] ] }, { "plaintext": " Fused (album), a 2005 album by Tony Iommi", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 4103518 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " The Fuse (Pennywise album), a 2005 album by Pennywise", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 1713993 ], "anchor_spans": [ [ 1, 27 ] ] }, { "plaintext": " F.U.S.E., an alias for electronic artist Richie Hawtin (born 1970)", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 180172 ], "anchor_spans": [ [ 1, 9 ] ] }, { "plaintext": " Fuse Festival, an Australian contemporary music event", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 16173284 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " \"Fuse\", an instrumental by Chaz Jankel from his 1980 album Chas Jankel", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 51502485 ], "anchor_spans": [ [ 60, 71 ] ] }, { "plaintext": " \"The Fuse\", a song by Bruce Springsteen from his 2002 album The Rising", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 538564 ], "anchor_spans": [ [ 61, 71 ] ] }, { "plaintext": " \"The Fuse\", a song by Jackson Browne from his 1976 album The Pretender", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 196502 ], "anchor_spans": [ [ 58, 71 ] ] }, { "plaintext": " \"The Fuse\", a song by Heaven 17 from their 1984 album How Men Are", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 6227158 ], "anchor_spans": [ [ 55, 66 ] ] }, { "plaintext": " Fuse (TV channel), an American cable television station", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 1559851 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Fuse (radio program), a musical radio program on CBC", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 3023715 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " The Fuse (game show), a UK game show broadcast on ITV1", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 26799250 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Fuse Games, a game developer", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 1949326 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Fuse (video game), a video game by Insomniac Games", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 32195372 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Fuse, a playable character in the game Apex Legends", "section_idx": 4, "section_name": "Entertainment", "target_page_ids": [ 59851379 ], "anchor_spans": [ [ 40, 52 ] ] }, { "plaintext": " Fuse, a consumer electronics company started by Tony Fadell", "section_idx": 5, "section_name": "Other uses", "target_page_ids": [ 1044721 ], "anchor_spans": [ [ 49, 60 ] ] }, { "plaintext": " Fuse (chocolate bar), a brand of chocolate bar made by Cadbury", "section_idx": 5, "section_name": "Other uses", "target_page_ids": [ 10234799 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Fuse (surname), a Japanese surname", "section_idx": 5, "section_name": "Other uses", "target_page_ids": [ 62886053 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Fuse, Shimane, a village located in Oki District, Shimane, Japan", "section_idx": 5, "section_name": "Other uses", "target_page_ids": [ 545709 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Scion Fuse, a concept car", "section_idx": 5, "section_name": "Other uses", "target_page_ids": [ 4884597 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Fews, Swedish-American rock band ", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 60033585 ], "anchor_spans": [ [ 1, 5 ] ] }, { "plaintext": " Flare, also known as a fusee", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 37708 ], "anchor_spans": [ [ 1, 6 ] ] }, { "plaintext": " Fusebox (programming)", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 962972 ], "anchor_spans": [ [ 1, 22 ] ] }, { "plaintext": " Fusee (disambiguation)", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 14119809 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Fusion (disambiguation)", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 10948 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Fuze (disambiguation)", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 11066619 ], "anchor_spans": [ [ 1, 22 ] ] } ]

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[ { "plaintext": "Garble may refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Garble (My Little Pony), a character in My Little Pony", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 5820208 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Garble, a character in Freddy and the Men from Mars", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 23928790 ], "anchor_spans": [ [ 24, 52 ] ] }, { "plaintext": " Grable, a surname (and list of people with the name)", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 27401703 ], "anchor_spans": [ [ 1, 7 ] ] } ]

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[ { "plaintext": "Gateway often refers to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A gate or portal", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 12821, 5185317 ], "anchor_spans": [ [ 2, 6 ], [ 10, 16 ] ] }, { "plaintext": "Gateway or The Gateway may also refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Gateway (film), a 1938 drama", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 48090940 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " The Gateway (2015 film), a horror film", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 51303170 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " The Gateway (2017 film), a science fiction film", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 62310791 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " The Gateway (2021 film), a crime thriller", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 67079248 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Gateway (band) a jazz trio featuring John Abercrombie, Jack DeJohnette and Dave Holland", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 651883 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Gateway (Gateway album) (1976)", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 24306712 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Gateway (Bongzilla album)", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 4982835 ], "anchor_spans": [ [ 1, 26 ] ] }, { "plaintext": " Gateway, an album by Erik Wøllo", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 17044465 ], "anchor_spans": [ [ 22, 32 ] ] }, { "plaintext": " Gateway (novel), a 1977 novel by Frederik Pohl", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 3786846 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Gateway (computer game), two adventure games based on the novel", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 728713 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Gateway (comics), a supporting character in Marvel's X-Men series", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 1911178 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Gateway (video game), an interactive fiction game", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 728713 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Gateway Galaxy, a galaxy in the video game Super Mario Galaxy", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 5076476 ], "anchor_spans": [ [ 44, 62 ] ] }, { "plaintext": " Gateway, a British science fiction imprint owned by Victor Gollancz Ltd", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 772804 ], "anchor_spans": [ [ 53, 72 ] ] }, { "plaintext": " Getaway, a 2014 four-issue comic book limited series published by IDW Publishing", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 943904 ], "anchor_spans": [ [ 67, 81 ] ] }, { "plaintext": " The Gateway, Nantwich, England", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 28345308 ], "anchor_spans": [ [ 1, 22 ] ] }, { "plaintext": " The Gateway, Hong Kong, Tsim Sha Tsui, Kowloon, Hong Kong, a shopping centre", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 3635006 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " The Gateway, Singapore, a twin-building office complex", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 11703212 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Gateway Theatre of Shopping, a shopping centre in uMhlanga, South Africa", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 1080563 ], "anchor_spans": [ [ 1, 28 ] ] }, { "plaintext": " Westfield Gateway, an enclosed shopping mall in Lincoln, Nebraska, United States", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 15034597 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " The Gateway (New Brunswick, New Jersey), New Jersey, United States", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 27078912 ], "anchor_spans": [ [ 1, 40 ] ] }, { "plaintext": " The Gateway (Salt Lake City), Salt Lake City, Utah, United States, a residential, retail and office complex", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 1182698 ], "anchor_spans": [ [ 1, 29 ] ] }, { "plaintext": " Gateway Sports and Entertainment Complex, a stadium complex in Cleveland, Ohio, United States", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 772969 ], "anchor_spans": [ [ 1, 41 ] ] }, { "plaintext": " Gateway Center (disambiguation)", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 10771780 ], "anchor_spans": [ [ 1, 32 ] ] }, { "plaintext": " Gateway Mall (disambiguation)", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 10115729 ], "anchor_spans": [ [ 1, 30 ] ] }, { "plaintext": " Gateway Theatre (disambiguation)", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 5740122 ], "anchor_spans": [ [ 1, 33 ] ] }, { "plaintext": " Gateway Tower (disambiguation)", "section_idx": 2, "section_name": "Buildings", "target_page_ids": [ 50813268 ], "anchor_spans": [ [ 1, 31 ] ] }, { "plaintext": " Gateway, Inc., a computer manufacturer", "section_idx": 3, "section_name": "Companies", "target_page_ids": [ 570838 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Gateway Newstands, a Canadian convenience store chain", "section_idx": 3, "section_name": "Companies", "target_page_ids": [ 24179013 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Gateway Supermarket, a former UK supermarket chain rebranded as Somerfield in the 1990s", "section_idx": 3, "section_name": "Companies", "target_page_ids": [ 1144728 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": " Gateway, Alaska, a census-designated place", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 105538 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Gateway, Arkansas, a town", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 106839 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Gateway, Los Angeles County, California, a place in California", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 2707512 ], "anchor_spans": [ [ 44, 63 ] ] }, { "plaintext": " Gateway, Nevada County, California, an unincorporated community", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 32208875 ], "anchor_spans": [ [ 1, 35 ] ] }, { "plaintext": " Gateway, San Diego, California, a neighborhood of San Diego", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 10838301 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Gateway, Colorado, an unincorporated community", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 8454505 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Gateway, Florida, a census-designated place", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 109331 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Gateway, Camden, a neighborhood of Camden, New Jersey", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 34527328 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Gateway, Oregon, an unincorporated community", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 34639005 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Gateway National Recreation Area, parks and beaches in New York City and New Jersey", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 418822 ], "anchor_spans": [ [ 1, 33 ] ] }, { "plaintext": " Gateway Region, the most urbanized part of northeastern New Jersey", "section_idx": 4, "section_name": "Places in the United States", "target_page_ids": [ 8546121 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Gateway Regional High School (Massachusetts)", "section_idx": 5, "section_name": "Schools in the United States", "target_page_ids": [ 18167906 ], "anchor_spans": [ [ 1, 45 ] ] }, { "plaintext": " Gateway Academy (Laredo, Texas), a charter high school in Laredo, Texas", "section_idx": 5, "section_name": "Schools in the United States", "target_page_ids": [ 30668237 ], "anchor_spans": [ [ 1, 32 ] ] }, { "plaintext": " Gateway Academy, Scottsdale, a private special school in Scottsdale, Arizona", "section_idx": 5, "section_name": "Schools in the United States", "target_page_ids": [ 11293184 ], "anchor_spans": [ [ 1, 28 ] ] }, { "plaintext": " Gateway International Raceway, a racetrack in Madison, Illinois, United States", "section_idx": 6, "section_name": "Sports", "target_page_ids": [ 1184858 ], "anchor_spans": [ [ 1, 30 ] ] }, { "plaintext": " Gateway Collegiate Athletic Conference, a women's sports conference that operated from 1983 to 1992 before being absorbed by the Missouri Valley Conference", "section_idx": 6, "section_name": "Sports", "target_page_ids": [ 38877871 ], "anchor_spans": [ [ 1, 39 ] ] }, { "plaintext": " Gateway Football Conference, a college football league now known as the Missouri Valley Football Conference", "section_idx": 6, "section_name": "Sports", "target_page_ids": [ 79394 ], "anchor_spans": [ [ 73, 108 ] ] }, { "plaintext": " Gateway (telecommunications), a network node equipped for interfacing with another network that uses different communication protocols", "section_idx": 7, "section_name": "Technology", "target_page_ids": [ 1338556 ], "anchor_spans": [ [ 1, 29 ] ] }, { "plaintext": " Gateway (web page), a web page designed to attract visitors and search engines to a particular website", "section_idx": 7, "section_name": "Technology", "target_page_ids": [ 2789866 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Gateway Technology, a cloning system in molecular biology", "section_idx": 7, "section_name": "Technology", "target_page_ids": [ 20579517 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Lunar Gateway, a planned moon orbit space station", "section_idx": 7, "section_name": "Technology", "target_page_ids": [ 53648310 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Gateway 3DS, a flash cartridge for the Nintendo 3DS; see Nintendo 3DS storage devices", "section_idx": 7, "section_name": "Technology", "target_page_ids": [ 1495667 ], "anchor_spans": [ [ 58, 86 ] ] }, { "plaintext": " Gateway Bridge (disambiguation)", "section_idx": 8, "section_name": "Transportation", "target_page_ids": [ 1793418 ], "anchor_spans": [ [ 1, 32 ] ] }, { "plaintext": " Gateway Motorway, a motorway in Brisbane", "section_idx": 8, "section_name": "Transportation", "target_page_ids": [ 2791746 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Gateway Boulevard, a major street in Edmonton, Alberta, Canada", "section_idx": 8, "section_name": "Transportation", "target_page_ids": [ 57011599 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Gateway Transportation Center, a rail and bus terminal station in downtown St. Louis, Missouri", "section_idx": 8, "section_name": "Transportation", "target_page_ids": [ 33307386 ], "anchor_spans": [ [ 1, 30 ] ] }, { "plaintext": " Gateway station (disambiguation)", "section_idx": 8, "section_name": "Transportation", "target_page_ids": [ 33202705 ], "anchor_spans": [ [ 1, 33 ] ] }, { "plaintext": " Gateway Project, a rail expansion project between New York City and Newark, New Jersey", "section_idx": 8, "section_name": "Transportation", "target_page_ids": [ 30791516 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " The Gateway (student magazine), the student magazine at the University of Alberta, Canada", "section_idx": 9, "section_name": "Other uses", "target_page_ids": [ 1855157 ], "anchor_spans": [ [ 1, 31 ] ] }, { "plaintext": " The Gateway (student newspaper), a UK student business and careers newspaper", "section_idx": 9, "section_name": "Other uses", "target_page_ids": [ 21624432 ], "anchor_spans": [ [ 1, 32 ] ] }, { "plaintext": " Greater Vancouver Gateway Program, an infrastructure project for Greater Vancouver", "section_idx": 9, "section_name": "Other uses", "target_page_ids": [ 9460075 ], "anchor_spans": [ [ 1, 34 ] ] }, { "plaintext": " Gateway Arch, St. Louis, Missouri, United States", "section_idx": 10, "section_name": "See also", "target_page_ids": [ 53353 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Gateway Church (disambiguation)", "section_idx": 10, "section_name": "See also", "target_page_ids": [ 32613355 ], "anchor_spans": [ [ 1, 32 ] ] }, { "plaintext": " Gateway drug theory, a hypothesis on drug use", "section_idx": 10, "section_name": "See also", "target_page_ids": [ 1197243 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": " Gateways (disambiguation)", "section_idx": 10, "section_name": "See also", "target_page_ids": [ 18536621 ], "anchor_spans": [ [ 1, 26 ] ] } ]

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[ { "plaintext": "Gating may refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Gating (electrophysiology), the opening (activation) or closing (deactivation) of ion channels ", "section_idx": 1, "section_name": "Neurobiology", "target_page_ids": [ 23965432 ], "anchor_spans": [ [ 0, 26 ] ] }, { "plaintext": "Sensory gating, an automatic process by which the brain adjusts to stimuli", "section_idx": 1, "section_name": "Neurobiology", "target_page_ids": [ 3619450 ], "anchor_spans": [ [ 0, 14 ] ] }, { "plaintext": "Synaptic gating, neural circuits suppressing inputs through synapses", "section_idx": 1, "section_name": "Neurobiology", "target_page_ids": [ 9916386 ], "anchor_spans": [ [ 0, 15 ] ] }, { "plaintext": "Gating (telecommunication), a process of selectively modifying signals", "section_idx": 2, "section_name": "Technology", "target_page_ids": [ 23965361 ], "anchor_spans": [ [ 0, 26 ] ] }, { "plaintext": "Gating system metalwork, a process in casting", "section_idx": 2, "section_name": "Technology", "target_page_ids": [ 53601 ], "anchor_spans": [ [ 0, 23 ] ] }, { "plaintext": "Gating signal, a signal that provides a time window ", "section_idx": 2, "section_name": "Technology", "target_page_ids": [ 9706285 ], "anchor_spans": [ [ 0, 13 ] ] }, { "plaintext": "Clock gating, a power-saving techniques used in synchronous circuits", "section_idx": 2, "section_name": "Technology", "target_page_ids": [ 2817754 ], "anchor_spans": [ [ 0, 12 ] ] }, { "plaintext": "Power gating, a power-saving technique for circuits ", "section_idx": 2, "section_name": "Technology", "target_page_ids": [ 25912566 ], "anchor_spans": [ [ 0, 12 ] ] }, { "plaintext": "Noise gate, a term in audio signal processing", "section_idx": 2, "section_name": "Technology", "target_page_ids": [ 1039345 ], "anchor_spans": [ [ 0, 10 ] ] }, { "plaintext": "Frequency-resolved optical gating, a term related to auto correlation in optics", "section_idx": 2, "section_name": "Technology", "target_page_ids": [ 2855589 ], "anchor_spans": [ [ 0, 33 ] ] }, { "plaintext": "Gating (punishment), a form of punishment used in educational establishments", "section_idx": 3, "section_name": "Other", "target_page_ids": [ 4745808 ], "anchor_spans": [ [ 0, 19 ] ] }, { "plaintext": "Gate (disambiguation)", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 1883286 ], "anchor_spans": [ [ 0, 21 ] ] }, { "plaintext": "Gates (disambiguation)", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 579784 ], "anchor_spans": [ [ 0, 22 ] ] } ]

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[ { "plaintext": "In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This fundamental (or TEM00) transverse Gaussian mode describes the intended output of most (but not all) lasers, as such a beam can be focused into the most concentrated spot. When such a beam is refocused by a lens, the transverse phase dependence is altered; this results in a different Gaussian beam. The electric and magnetic field amplitude profiles along any such circular Gaussian beam (for a given wavelength and polarization) are determined by a single parameter: the so-called Beam waist . At any position relative to the waist (focus) along a beam having a specified , the field amplitudes and phases are thereby determined as detailed Mathematical form.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 22483, 1612888, 9426, 261993, 27367275, 245552, 556970, 516150, 17556, 18320, 41092, 36563, 33125, 41564 ], "anchor_spans": [ [ 3, 9 ], [ 32, 36 ], [ 40, 65 ], [ 76, 92 ], [ 99, 117 ], [ 156, 173 ], [ 204, 213 ], [ 264, 274 ], [ 341, 346 ], [ 447, 451 ], [ 544, 552 ], [ 557, 571 ], [ 642, 652 ], [ 657, 669 ] ] }, { "plaintext": "The equations below assume a beam with a circular cross-section at all values of ; this can be seen by noting that a single transverse dimension, , appears. Beams with elliptical cross-sections, or with waists at different positions in for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of and of the location for the two transverse dimensions and .", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10225, 585614 ], "anchor_spans": [ [ 169, 179 ], [ 273, 283 ] ] }, { "plaintext": "Arbitrary solutions of the paraxial Helmholtz equation can be expressed as combinations of Hermite-Gaussian modes (whose amplitude profiles are separable in and using Cartesian coordinates) or similarly as combinations of Laguerre-Gaussian modes (whose amplitude profiles are separable in and using cylindrical coordinates). At any point along the beam these modes include the same Gaussian factor as the fundamental Gaussian mode multiplying the additional geometrical factors for the specified mode. However different modes propagate with a different Gouy phase which is why the net transverse profile due to a superposition of modes evolves in , whereas the propagation of any single Hermite–Gaussian (or Laguerre–Gaussian) mode retains the same form along a beam.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 1156215, 7706, 176733, 1201321 ], "anchor_spans": [ [ 27, 54 ], [ 169, 190 ], [ 304, 327 ], [ 619, 632 ] ] }, { "plaintext": "Although there are other possible modal decompositions, these families of solutions are the most useful for problems involving compact beams, that is, where the optical power is rather closely confined along an axis. Even when a laser is not operating in the fundamental Gaussian mode, its power will generally be found among the lowest-order modes using these decompositions, as the spatial extent of higher order modes will tend to exceed the bounds of a laser's resonator (cavity). \"Gaussian beam\" normally implies radiation confined to the fundamental (TEM00) Gaussian mode.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 516150, 591513 ], "anchor_spans": [ [ 34, 54 ], [ 465, 474 ] ] }, { "plaintext": "The Gaussian beam is a transverse electromagnetic (TEM) mode. The mathematical expression for the electric field amplitude is a solution to the paraxial Helmholtz equation. Assuming polarization in the direction and propagation in the direction, the electric field in phasor (complex) notation is given by:", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 516150, 1156215, 1256073 ], "anchor_spans": [ [ 23, 60 ], [ 144, 171 ], [ 270, 276 ] ] }, { "plaintext": "where", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the radial distance from the center axis of the beam,", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the axial distance from the beam's focus (or \"waist\"),", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the imaginary unit,", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 52358 ], "anchor_spans": [ [ 8, 22 ] ] }, { "plaintext": " is the wave number (in radians per meter) for a free-space wavelength , and is the index of refraction of the medium in which the beam propagates,", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 164570, 26003 ], "anchor_spans": [ [ 8, 19 ], [ 24, 30 ] ] }, { "plaintext": ", the electric field amplitude (and phase) at the origin (, ),", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the radius at which the field amplitudes fall to of their axial values (i.e., where the intensity values fall to of their axial values), at the plane along the beam,", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the Beam waist,", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the Wavefront curvature of the beam's wavefronts at , and", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 1484541 ], "anchor_spans": [ [ 42, 51 ] ] }, { "plaintext": " is the Gouy phase at , an extra phase term beyond that attributable to the phase velocity of light.", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 25098 ], "anchor_spans": [ [ 76, 90 ] ] }, { "plaintext": "There is also an understood time dependence multiplying such phasor quantities; the actual field at a point in time and space is given by the real part of that complex quantity. This time factor involves an arbitrary sign convention, as discussed at .", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 1256073, 5826, 293533 ], "anchor_spans": [ [ 62, 68 ], [ 143, 152 ], [ 218, 233 ] ] }, { "plaintext": "Since this solution relies on the paraxial approximation, it is not accurate for very strongly diverging beams. The above form is valid in most practical cases, where .", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The corresponding intensity (or irradiance) distribution is given by", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 41993, 556970 ], "anchor_spans": [ [ 18, 27 ], [ 32, 42 ] ] }, { "plaintext": "where the constant is the wave impedance of the medium in which the beam is propagating. For free space, ≈ 377 Ω. is the intensity at the center of the beam at its waist. ", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 41864 ], "anchor_spans": [ [ 27, 41 ] ] }, { "plaintext": "If is the total power of the beam,", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 24236 ], "anchor_spans": [ [ 17, 22 ] ] }, { "plaintext": "At a position along the beam (measured from the focus), the spot size parameter is given by a hyperbolic relation:", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 14052 ], "anchor_spans": [ [ 96, 115 ] ] }, { "plaintext": "where", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "is called the Rayleigh range as further discussed below, and is the refractive index of the medium.", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 8454507 ], "anchor_spans": [ [ 14, 28 ] ] }, { "plaintext": "The radius of the beam , at any position along the beam, is related to the full width at half maximum (FWHM) of the intensity distribution at that position according to:", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 41200 ], "anchor_spans": [ [ 76, 102 ] ] }, { "plaintext": "The curvature of the wavefronts is largest at the Rayleigh distance, , on either side of the waist, crossing zero at the waist itself. Beyond the Rayleigh distance, , it again decreases in magnitude, approaching zero as . The curvature is often expressed in terms of its reciprocal, , the radius of curvature; for a fundamental Gaussian beam the curvature at position is given by:", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 4463104 ], "anchor_spans": [ [ 289, 308 ] ] }, { "plaintext": "so the radius of curvature is ", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Being the reciprocal of the curvature, the radius of curvature reverses sign and is infinite at the beam waist where the curvature goes through zero.", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The Gouy phase is a phase advance gradually acquired by a beam around the focal region. At position the Gouy phase of a fundamental Gaussian beam is given by", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 14933128 ], "anchor_spans": [ [ 4, 8 ] ] }, { "plaintext": "The Gouy phase results in an increase in the apparent wavelength near the waist (). Thus the phase velocity in that region formally exceeds the speed of light. That paradoxical behavior must be understood as a near-field phenomenon where the departure from the phase velocity of light (as would apply exactly to a plane wave) is very small except in the case of a beam with large numerical aperture, in which case the wavefronts' curvature (see previous section) changes substantially over the distance of a single wavelength. In all cases the wave equation is satisfied at every position.", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [ 271708, 41432, 1156215 ], "anchor_spans": [ [ 211, 221 ], [ 381, 399 ], [ 545, 558 ] ] }, { "plaintext": "The sign of the Gouy phase depends on the sign convention chosen for the electric field phasor. With dependence, the Gouy phase changes from to , while with dependence it changes from to along the axis.", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For a fundamental Gaussian beam, the Gouy phase results in a net phase discrepancy with respect to the speed of light amounting to radians (thus a phase reversal) as one moves from the far field on one side of the waist to the far field on the other side. This phase variation is not observable in most experiments. It is, however, of theoretical importance and takes on a greater range for Laguerre-Gaussian modes.", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Many laser beams have an elliptical cross-section. Also common are beams with waist positions which are different for the two transverse dimensions, called astigmatic beams. These beams can be dealt with using the above two evolution equations, but with distinct values of each parameter for and and distinct definitions of the point. The Gouy phase is a single value calculated correctly by summing the contribution from each dimension, with a Gouy phase within the range contributed by each dimension.", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "An elliptical beam will invert its ellipticity ratio as it propagates from the far field to the waist. The dimension which was the larger far from the waist, will be the smaller near the waist.", "section_idx": 1, "section_name": "Mathematical form", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The geometric dependence of the fields of a Gaussian beam are governed by the light's wavelength (in the dielectric medium, if not free space) and the following beam parameters, all of which are connected as detailed in the following sections.", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The shape of a Gaussian beam of a given wavelength is governed solely by one parameter, the beam waist . This is a measure of the beam size at the point of its focus ( in the above equations) where the beam width (as defined above) is the smallest (and likewise where the intensity on-axis () is the largest). From this parameter the other parameters describing the beam geometry are determined. This includes the Rayleigh range and asymptotic beam divergence , as detailed below.", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [ 8454507 ], "anchor_spans": [ [ 416, 430 ] ] }, { "plaintext": "The Rayleigh distance or Rayleigh range is determined given a Gaussian beam's waist size:", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Here is the wavelength of the light, is the index of refraction. At a distance from the waist equal to the Rayleigh range , the width of the beam is larger than it is at the focus where , the beam waist. That also implies that the on-axis () intensity there is one half of the peak intensity (at ). That point along the beam also happens to be where the wavefront curvature () is greatest.", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The distance between the two points is called the confocal parameter or depth of focus of the beam.", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Although the tails of a Gaussian function never actually reach zero, for the purposes of the following discussion the \"edge\" of a beam is considered to be the radius where . That is where the intensity has dropped to of its on-axis value. Now, for the parameter increases linearly with . This means that far from the waist, the beam \"edge\" (in the above sense) is cone-shaped. The angle between that cone (whose ) and the beam axis () defines the divergence of the beam:", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In the paraxial case, as we have been considering, (in radians) is then approximately", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where is the refractive index of the medium the beam propagates through, and is the free-space wavelength. The total angular spread of the diverging beam, or apex angle of the above-described cone, is then given by", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "That cone then contains 86% of the Gaussian beam's total power.", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Because the divergence is inversely proportional to the spot size, for a given wavelength , a Gaussian beam that is focused to a small spot diverges rapidly as it propagates away from the focus. Conversely, to minimize the divergence of a laser beam in the far field (and increase its peak intensity at large distances) it must have a large cross-section () at the waist (and thus a large diameter where it is launched, since is never less than ). This relationship between beam width and divergence is a fundamental characteristic of diffraction, and of the Fourier transform which describes Fraunhofer diffraction. A beam with any specified amplitude profile also obeys this inverse relationship, but the fundamental Gaussian mode is a special case where the product of beam size at focus and far-field divergence is smaller than for any other case.", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [ 8603, 52247, 799986 ], "anchor_spans": [ [ 536, 547 ], [ 560, 577 ], [ 594, 616 ] ] }, { "plaintext": "Since the Gaussian beam model uses the paraxial approximation, it fails when wavefronts are tilted by more than about 30° from the axis of the beam. From the above expression for divergence, this means the Gaussian beam model is only accurate for beams with waists larger than about .", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Laser beam quality is quantified by the beam parameter product (BPP). For a Gaussian beam, the BPP is the product of the beam's divergence and waist size . The BPP of a real beam is obtained by measuring the beam's minimum diameter and far-field divergence, and taking their product. The ratio of the BPP of the real beam to that of an ideal Gaussian beam at the same wavelength is known as (\"M squared\"). The for a Gaussian beam is one. All real laser beams have values greater than one, although very high quality beams can have values very close to one.", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [ 30206715, 4443719, 4443796 ], "anchor_spans": [ [ 0, 18 ], [ 40, 62 ], [ 394, 403 ] ] }, { "plaintext": "The numerical aperture of a Gaussian beam is defined to be , where is the index of refraction of the medium through which the beam propagates. This means that the Rayleigh range is related to the numerical aperture by ", "section_idx": 2, "section_name": "Beam parameters", "target_page_ids": [ 41432, 25880 ], "anchor_spans": [ [ 4, 22 ], [ 75, 94 ] ] }, { "plaintext": "With a beam centered on an aperture, the power passing through a circle of radius in the transverse plane at position is", "section_idx": 3, "section_name": "Power and intensity", "target_page_ids": [ 47474, 24236 ], "anchor_spans": [ [ 27, 35 ], [ 41, 46 ] ] }, { "plaintext": "where", "section_idx": 3, "section_name": "Power and intensity", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "is the total power transmitted by the beam.", "section_idx": 3, "section_name": "Power and intensity", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For a circle of radius , the fraction of power transmitted through the circle is", "section_idx": 3, "section_name": "Power and intensity", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Similarly, about 90% of the beam's power will flow through a circle of radius , 95% through a circle of radius , and 99% through a circle of radius .", "section_idx": 3, "section_name": "Power and intensity", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The peak intensity at an axial distance from the beam waist can be calculated as the limit of the enclosed power within a circle of radius , divided by the area of the circle as the circle shrinks:", "section_idx": 3, "section_name": "Power and intensity", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The limit can be evaluated using L'Hôpital's rule:", "section_idx": 3, "section_name": "Power and intensity", "target_page_ids": [ 18531 ], "anchor_spans": [ [ 33, 49 ] ] }, { "plaintext": "The spot size and curvature of a Gaussian beam as a function of along the beam can also be encoded in the complex beam parameter given by:", "section_idx": 4, "section_name": "Complex beam parameter", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Introducing this complication leads to a simplification of the Gaussian beam field equation as shown below. It can be seen that the reciprocal of contains the wavefront curvature and relative on-axis intensity in its real and imaginary parts, respectively:", "section_idx": 4, "section_name": "Complex beam parameter", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The complex beam parameter simplifies the mathematical analysis of Gaussian beam propagation, and especially in the analysis of optical resonator cavities using ray transfer matrices.", "section_idx": 4, "section_name": "Complex beam parameter", "target_page_ids": [ 591513, 172317 ], "anchor_spans": [ [ 128, 154 ], [ 161, 182 ] ] }, { "plaintext": "Then using this form, the earlier equation for the electric (or magnetic) field is greatly simplified. If we call the relative field strength of an elliptical Gaussian beam (with the elliptical axes in the and directions) then it can be separated in and according to:", "section_idx": 4, "section_name": "Complex beam parameter", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where ", "section_idx": 4, "section_name": "Complex beam parameter", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where and are the complex beam parameters in the and directions.", "section_idx": 4, "section_name": "Complex beam parameter", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For the common case of a circular beam profile, and , which yields", "section_idx": 4, "section_name": "Complex beam parameter", "target_page_ids": [ 2217599 ], "anchor_spans": [ [ 25, 46 ] ] }, { "plaintext": "When a gaussian beam propagates through a thin lens, the outgoing beam is also a (different) gaussian beam, provided that the beam travels along the cylindrical symmetry axis of the lens. The focal length of the lens , the beam waist radius , and beam waist position of the incoming beam can be used to determine the beam waist radius and position of the outgoing beam.", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [ 3331499 ], "anchor_spans": [ [ 42, 51 ] ] }, { "plaintext": "As derived by Saleh and Teich, the relationship between the ingoing and outgoing beams can be found by considering the phase that is added to each point of the gaussian beam as it travels through the lens. An alternative approach due to Self is to consider the effect of a thin lens on the gaussian beam wavefronts.", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [ 24047, 1484541 ], "anchor_spans": [ [ 119, 124 ], [ 306, 316 ] ] }, { "plaintext": "The exact solution to the above problem is expressed simply in terms of the magnification ", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The magnification, which depends on and , is given by", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "An equivalent expression for the beam position is", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "This last expression makes clear that the ray optics thin lens equation is recovered in the limit that . It can also be noted that if then the incoming beam is \"well collimated\" so that .", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [ 3331499 ], "anchor_spans": [ [ 53, 71 ] ] }, { "plaintext": "In some applications it is desirable to use a converging lens to focus a laser beam to a very small spot. Mathematically, this implies minimization of the magnification . If the beam size is constrained by the size of available optics, this is typically best achieved by sending the largest possible collimated beam through a small focal length lens, i.e. by maximizing and minimizing . In this situation, it is justifiable to make the approximation , implying that and yielding the result . This result is often presented in the form", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "which is found after assuming that the medium has index of refraction and substituting . The factors of 2 are introduced because of a common preference to represent beam size by the beam waist diameters and , rather than the waist radii and .", "section_idx": 5, "section_name": "Beam optics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "As a special case of electromagnetic radiation, Gaussian beams (and the higher-order Gaussian modes detailed below) are solutions to the wave equation for an electromagnetic field in free space or in a homogeneous dielectric medium, obtained by combining Maxwell's equations for the curl of and the curl of , resulting in: ", "section_idx": 6, "section_name": "Wave equation", "target_page_ids": [ 9426, 2924436 ], "anchor_spans": [ [ 21, 46 ], [ 137, 179 ] ] }, { "plaintext": "where is the speed of light in the medium, and could either refer to the electric or magnetic field vector, as any specific solution for either determines the other. The Gaussian beam solution is valid only in the paraxial approximation, that is, where wave propagation is limited to directions within a small angle of an axis. Without loss of generality let us take that direction to be the direction in which case the solution can generally be written in terms of which has no time dependence and varies relatively smoothly in space, with the main variation spatially corresponding to the wavenumber in the direction:", "section_idx": 6, "section_name": "Wave equation", "target_page_ids": [ 2643603, 164570 ], "anchor_spans": [ [ 216, 224 ], [ 596, 606 ] ] }, { "plaintext": "Using this form along with the paraxial approximation, can then be essentially neglected. Since solutions of the electromagnetic wave equation only hold for polarizations which are orthogonal to the direction of propagation (), we have without loss of generality considered the polarization to be in the direction so that we now solve a scalar equation for .", "section_idx": 6, "section_name": "Wave equation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Substituting this solution into the wave equation above yields the paraxial approximation to the scalar wave equation:", "section_idx": 6, "section_name": "Wave equation", "target_page_ids": [ 1156215 ], "anchor_spans": [ [ 67, 89 ] ] }, { "plaintext": "Writing the wave equations in the light-cone coordinates returns this equation without utilizing any approximation. Gaussian beams of any beam waist satisfy the paraxial approximation to the scalar wave equation; this is most easily verified by expressing the wave at in terms of the complex beam parameter as defined above. There are many other solutions. As solutions to a linear system, any combination of solutions (using addition or multiplication by a constant) is also a solution. The fundamental Gaussian happens to be the one that minimizes the product of minimum spot size and far-field divergence, as noted above. In seeking paraxial solutions, and in particular ones that would describe laser radiation that is not in the fundamental Gaussian mode, we will look for families of solutions with gradually increasing products of their divergences and minimum spot sizes. Two important orthogonal decompositions of this sort are the Hermite–Gaussian or Laguerre-Gaussian modes, corresponding to rectangular and circular symmetry respectively, as detailed in the next section. With both of these, the fundamental Gaussian beam we have been considering is the lowest order mode.", "section_idx": 6, "section_name": "Wave equation", "target_page_ids": [ 17785091, 722503 ], "anchor_spans": [ [ 34, 56 ], [ 378, 391 ] ] }, { "plaintext": "It is possible to decompose a coherent paraxial beam using the orthogonal set of so-called Hermite-Gaussian modes, any of which are given by the product of a factor in and a factor in . Such a solution is possible due to the separability in and in the paraxial Helmholtz equation as written in Cartesian coordinates. Thus given a mode of order referring to the and directions, the electric field amplitude at may be given by:", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 1156215, 7706 ], "anchor_spans": [ [ 255, 282 ], [ 297, 318 ] ] }, { "plaintext": "where the factors for the and dependence are each given by:", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where we have employed the complex beam parameter (as defined above) for a beam of waist at from the focus. In this form, the first factor is just a normalizing constant to make the set of orthonormal. The second factor is an additional normalization dependent on which compensates for the expansion of the spatial extent of the mode according to (due to the last two factors). It also contains part of the Gouy phase. The third factor is a pure phase which enhances the Gouy phase shift for higher orders .", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 194743 ], "anchor_spans": [ [ 193, 204 ] ] }, { "plaintext": "The final two factors account for the spatial variation over (or ). The fourth factor is the Hermite polynomial of order (\"physicists' form\", i.e. ), while the fifth accounts for the Gaussian amplitude fall-off , although this isn't obvious using the complex in the exponent. Expansion of that exponential also produces a phase factor in which accounts for the wavefront curvature () at along the beam.", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 195984 ], "anchor_spans": [ [ 94, 112 ] ] }, { "plaintext": "Hermite-Gaussian modes are typically designated \"TEMlm\"; the fundamental Gaussian beam may thus be referred to as TEM00 (where TEM is transverse electro-magnetic). Multiplying and to get the 2-D mode profile, and removing the normalization so that the leading factor is just called , we can write the mode in the more accessible form:", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 516150 ], "anchor_spans": [ [ 134, 161 ] ] }, { "plaintext": "In this form, the parameter , as before, determines the family of modes, in particular scaling the spatial extent of the fundamental mode's waist and all other mode patterns at . Given that , and have the same definitions as for the fundamental Gaussian beam described Evolving beam width. It can be seen that with we obtain the fundamental Gaussian beam described earlier (since ). The only specific difference in the and profiles at any are due to the Hermite polynomial factors for the order numbers and . However, there is a change in the evolution of the modes' Gouy phase over :", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where the combined order of the mode is defined as . While the Gouy phase shift for the fundamental (0,0) Gaussian mode only changes by radians over all of (and only by radians between ), this is increased by the factor for the higher order modes.", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Hermite Gaussian modes, with their rectangular symmetry, are especially suited for the modal analysis of radiation from lasers whose cavity design is asymmetric in a rectangular fashion. On the other hand, lasers and systems with circular symmetry can better be handled using the set of Laguerre-Gaussian modes introduced in the next section.", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Beam profiles which are circularly symmetric (or lasers with cavities that are cylindrically symmetric) are often best solved using the Laguerre-Gaussian modal decomposition. These functions are written in cylindrical coordinates using generalized Laguerre polynomials. Each transverse mode is again labelled using two integers, in this case the radial index and the azimuthal index which can be positive or negative (or zero):", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 176733, 943917 ], "anchor_spans": [ [ 208, 231 ], [ 238, 270 ] ] }, { "plaintext": "where are the generalized Laguerre polynomials. is a required normalization constant:", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 943917 ], "anchor_spans": [ [ 15, 47 ] ] }, { "plaintext": ".", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " and have the same definitions as Beam parameters. As with the higher-order Hermite-Gaussian modes the magnitude of the Laguerre-Gaussian modes' Gouy phase shift is exaggerated by the factor :", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where in this case the combined mode number . As before, the transverse amplitude variations are contained in the last two factors on the upper line of the equation, which again includes the basic Gaussian drop off in but now multiplied by a Laguerre polynomial. The effect of the rotational mode number , in addition to affecting the Laguerre polynomial, is mainly contained in the phase factor , in which the beam profile is advanced (or retarded) by complete phases in one rotation around the beam (in ). This is an example of an optical vortex of topological charge , and can be associated with the orbital angular momentum of light in that mode.", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 531239, 3065940, 33190076 ], "anchor_spans": [ [ 282, 297 ], [ 536, 550 ], [ 606, 639 ] ] }, { "plaintext": "In elliptic coordinates, one can write the higher-order modes using Ince polynomials. The even and odd Ince-Gaussian modes are given by", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 5006562, 33358296 ], "anchor_spans": [ [ 3, 23 ], [ 68, 83 ] ] }, { "plaintext": "where and are the radial and angular elliptic coordinates defined by", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " are the even Ince polynomials of order and degree where is the ellipticity parameter. The Hermite-Gaussian and Laguerre-Gaussian modes are a special case of the Ince-Gaussian modes for and respectively.", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "There is another important class of paraxial wave modes in cylindrical coordinates in which the complex amplitude is proportional to a confluent hypergeometric function.", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 176733, 1256073, 1516095 ], "anchor_spans": [ [ 59, 82 ], [ 96, 113 ], [ 135, 168 ] ] }, { "plaintext": "These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. Their intensity profiles are characterized by a single brilliant ring; like Laguerre–Gaussian modes, their intensities fall to zero at the center (on the optical axis) except for the fundamental (0,0) mode. A mode's complex amplitude can be written in terms of the normalized (dimensionless) radial coordinate and the normalized longitudinal coordinate as follows:", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [ 54240, 228601, 33190076 ], "anchor_spans": [ [ 19, 27 ], [ 50, 63 ], [ 72, 103 ] ] }, { "plaintext": "where the rotational index is an integer, and is real-valued, is the gamma function and is a confluent hypergeometric function.", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Some subfamilies of hypergeometric-Gaussian (HyGG) modes can be listed as the modified Bessel-Gaussian modes, the modified exponential Gaussian modes, and the modified Laguerre–Gaussian modes.", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The set of hypergeometric-Gaussian modes is overcomplete and is not an orthogonal set of modes. In spite of its complicated field profile, HyGG modes have a very simple profile at the beam waist ():", "section_idx": 7, "section_name": "Higher-order modes", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Bessel beam", "section_idx": 8, "section_name": "See also", "target_page_ids": [ 9071326 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Tophat beam", "section_idx": 8, "section_name": "See also", "target_page_ids": [ 12524280 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Laser beam profiler", "section_idx": 8, "section_name": "See also", "target_page_ids": [ 15267398 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": " Quasioptics", "section_idx": 8, "section_name": "See also", "target_page_ids": [ 35183128 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Chapter 5, \"Optical Beams,\" pp.267.", "section_idx": 10, "section_name": "References", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Chapter 3, \"Beam Optics,\" pp.80–107.", "section_idx": 10, "section_name": "References", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Chapter 16.", "section_idx": 10, "section_name": "References", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Gaussian Beam Optics Tutorial, Newport", "section_idx": 11, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Physical_optics", "Laser_science", "Electromagnetic_radiation" ]

[]

[ { "plaintext": "A gel is a semi-solid that can have properties ranging from soft and weak to hard and tough. Gels are defined as a substantially dilute cross-linked system, which exhibits no flow when in the steady-state, although the liquid phase may still diffuse through this system. A gel has been defined phenomenologically as a soft, solid or solid-like material consisting of two or more components, one of which is a liquid, present in substantial quantity.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 4449204, 1089106 ], "anchor_spans": [ [ 11, 21 ], [ 136, 146 ] ] }, { "plaintext": "By weight, gels are mostly liquid, yet they behave like solids because of a three-dimensional cross-linked network within the liquid. It is the crosslinking within the fluid that gives a gel its structure (hardness) and contributes to the adhesive stick (tack). In this way, gels are a dispersion of molecules of a liquid within a solid medium. The word gel was coined by 19th-century Scottish chemist Thomas Graham by clipping from gelatine.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 2396, 48205, 2263849, 13160 ], "anchor_spans": [ [ 255, 259 ], [ 402, 415 ], [ 419, 427 ], [ 433, 441 ] ] }, { "plaintext": "The process of forming a gel is called gelation.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 21301778 ], "anchor_spans": [ [ 39, 47 ] ] }, { "plaintext": "Gels consist of a solid three-dimensional network that spans the volume of a liquid medium and ensnares it through surface tension effects. This internal network structure may result from physical bonds (physical gels) or chemical bonds (chemical gels), as well as crystallites or other junctions that remain intact within the extending fluid. Virtually any fluid can be used as an extender including water (hydrogels), oil, and air (aerogel). Both by weight and volume, gels are mostly fluid in composition and thus exhibit densities similar to those of their constituent liquids. Edible jelly is a common example of a hydrogel and has approximately the density of water.", "section_idx": 2, "section_name": "Composition", "target_page_ids": [ 113302, 5993, 365435, 844290, 50069638 ], "anchor_spans": [ [ 115, 130 ], [ 222, 235 ], [ 265, 276 ], [ 408, 416 ], [ 434, 441 ] ] }, { "plaintext": "Polyionic polymers are polymers with an ionic functional group. The ionic charges prevent the formation of tightly coiled polymer chains. This allows them to contribute more to viscosity in their stretched state, because the stretched-out polymer takes up more space. This is also the reason gel hardens. See polyelectrolyte for more information.", "section_idx": 2, "section_name": "Composition", "target_page_ids": [ 18963754, 1225002 ], "anchor_spans": [ [ 177, 186 ], [ 309, 324 ] ] }, { "plaintext": "A colloidal gel consists of a percolated network of particles in a fluid medium. This network gives the material its mechanical properties. The particles can show attractive interactions through osmotic depletion, or through polymeric links. Colloidal gels have three phases in their lifespan: gelation, aging and collapse. The gel is initially formed by the assembly of particles into a space-spanning network, leading to a phase arrest. In the aging phase, the particle slowly rearrange to form thicker strands, increasing the elasticity of the material. Gels can also be collapsed and separated by external fields such as gravity. Colloidal gels show linear response rheology at low amplitudes. These materials have been explored as candidates for a drug release matrix. ", "section_idx": 3, "section_name": "Types", "target_page_ids": [ 5346, 187805, 25453, 39639151 ], "anchor_spans": [ [ 2, 9 ], [ 30, 40 ], [ 118, 139 ], [ 196, 213 ] ] }, { "plaintext": "A hydrogel is a network of polymer chains that are hydrophilic, sometimes found as a colloidal gel in which water is the dispersion medium. A three-dimensional solid results from the hydrophilic polymer chains being held together by cross-links. Because of the inherent cross-links, the structural integrity of the hydrogel network does not dissolve from the high concentration of water. Hydrogels are highly absorbent (they can contain over 90% water) natural or synthetic polymeric networks.", "section_idx": 3, "section_name": "Types", "target_page_ids": [ 844290, 5346, 1383986 ], "anchor_spans": [ [ 2, 10 ], [ 85, 92 ], [ 409, 418 ] ] }, { "plaintext": "Hydrogels also possess a degree of flexibility very similar to natural tissue, due to their significant water content. As responsive \"smart materials,\" hydrogels can encapsulate chemical systems which upon stimulation by external factors such as a change of pH may cause specific compounds such as glucose to be liberated to the environment, in most cases by a gel-sol transition to the liquid state. Chemomechanical polymers are mostly also hydrogels, which upon stimulation change their volume and can serve as actuators or sensors. The first appearance of the term 'hydrogel' in the literature was in 1894.", "section_idx": 3, "section_name": "Types", "target_page_ids": [ 1065009, 1701055, 293079, 235757 ], "anchor_spans": [ [ 134, 149 ], [ 361, 379 ], [ 513, 522 ], [ 526, 533 ] ] }, { "plaintext": "An organogel is a non-crystalline, non-glassy thermoreversible (thermoplastic) solid material composed of a liquid organic phase entrapped in a three-dimensionally cross-linked network. The liquid can be, for example, an organic solvent, mineral oil, or vegetable oil. The solubility and particle dimensions of the structurant are important characteristics for the elastic properties and firmness of the organogel. Often, these systems are based on self-assembly of the structurant molecules. (An example of formation of an undesired thermoreversible network is the occurrence of wax crystallization in petroleum.)", "section_idx": 3, "section_name": "Types", "target_page_ids": [ 2119658, 12581, 182444, 18993825, 22203, 37431, 212419, 192331, 59497, 268923, 351914, 23195 ], "anchor_spans": [ [ 18, 33 ], [ 35, 45 ], [ 64, 77 ], [ 108, 114 ], [ 115, 122 ], [ 221, 236 ], [ 238, 249 ], [ 254, 267 ], [ 273, 283 ], [ 365, 372 ], [ 449, 462 ], [ 603, 612 ] ] }, { "plaintext": "Organogels have potential for use in a number of applications, such as in pharmaceuticals, cosmetics, art conservation, and food.", "section_idx": 3, "section_name": "Types", "target_page_ids": [ 920218 ], "anchor_spans": [ [ 74, 89 ] ] }, { "plaintext": "A xerogel is a solid formed from a gel by drying with unhindered shrinkage. Xerogels usually retain high porosity (15–50%) and enormous surface area (150–900 m2/g), along with very small pore size (1–10nm). When solvent removal occurs under supercritical conditions, the network does not shrink and a highly porous, low-density material known as an aerogel is produced. Heat treatment of a xerogel at elevated temperature produces viscous sintering (shrinkage of the xerogel due to a small amount of viscous flow) which results in a denser and more robust solid, the density and porosity achieved depend on the sintering conditions.", "section_idx": 3, "section_name": "Types", "target_page_ids": [ 19461794, 37431, 762691, 50069638, 145020 ], "anchor_spans": [ [ 188, 192 ], [ 213, 220 ], [ 242, 255 ], [ 350, 357 ], [ 440, 449 ] ] }, { "plaintext": "Nanocomposite hydrogels or hybrid hydrogels, are highly hydrated polymeric networks, either physically or covalently crosslinked with each other and/or with nanoparticles or nanostructures. Nanocomposite hydrogels can mimic native tissue properties, structure and microenvironment due to their hydrated and interconnected porous structure. A wide range of nanoparticles, such as carbon-based, polymeric, ceramic, and metallic nanomaterials can be incorporated within the hydrogel structure to obtain nanocomposites with tailored functionality. Nanocomposite hydrogels can be engineered to possess superior physical, chemical, electrical, thermal, and biological properties.", "section_idx": 3, "section_name": "Types", "target_page_ids": [ 45160933 ], "anchor_spans": [ [ 0, 23 ] ] }, { "plaintext": "Many gels display thixotropy – they become fluid when agitated, but resolidify when resting.", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 817680 ], "anchor_spans": [ [ 18, 28 ] ] }, { "plaintext": "In general, gels are apparently solid, jelly-like materials. It is a type of non-Newtonian fluid.", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 75367 ], "anchor_spans": [ [ 77, 96 ] ] }, { "plaintext": "By replacing the liquid with gas it is possible to prepare aerogels, materials with exceptional properties including very low density, high specific surface areas, and excellent thermal insulation properties.", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 50069638, 8390819 ], "anchor_spans": [ [ 59, 66 ], [ 135, 162 ] ] }, { "plaintext": "A gel is in essence the mixture of a polymer network and a solvent phase. Upon stretching, the network crosslinks are moved further apart from each other. Due to the polymer strands between crosslinks act as entropic springs, gels demonstrate elasticity like rubber (which is just a polymer network, without solvent). This is so because the free energy penalty to stretch an ideal polymer segment monomers of size between crosslinks to an end-to-end distance is approximately given by ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 37431, 1089106, 2025734, 7623862, 39221, 2537711, 18525261 ], "anchor_spans": [ [ 59, 66 ], [ 103, 113 ], [ 208, 224 ], [ 259, 265 ], [ 341, 352 ], [ 375, 388 ], [ 441, 460 ] ] }, { "plaintext": "This is the origin of both gel and rubber elasticity. But one key difference is that gel contains an additional solvent phase and hence is capable of having significant volume changes under deformation by taking in and out solvent. For example, a gel could swell to several times its initial volume after being immersed in a solvent after equilibrium is reached. This is the phenomenon of gel swelling. On the contrary, if we take the swelled gel out and allow the solvent to evaporate, the gel would shrink to roughly its original size. This gel volume change can alternatively be introduced by applying external forces. If a uniaxial compressive stress is applied to a gel, some solvent contained in the gel would be squeezed out and the gel shrinks in the applied-stress direction. To study the gel mechanical state in equilibrium, a good starting point is to consider a cubic gel of volume that is stretched by factors , and in the three orthogonal directions during swelling after being immersed in a solvent phase of initial volume . The final deformed volume of gel is then and the total volume of the system is that is assumed constant during the swelling process for simplicity of treatment. The swelled state of the gel is now completely characterized by stretch factors , and and hence it is of interest to derive the deformation free energy as a function of them, denoted as . For analogy to the historical treatment of rubber elasticity and mixing free energy, is most often defined as the free energy difference after and before the swelling normalized by the initial gel volume , that is, a free energy difference density. The form of naturally assumes two contributions of radically different physical origins, one is associated with the elastic deformation of the polymer network, and the other with the mixing of the network with the solvent. Hence, we write ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 7623862, 19194778, 228107, 19194778, 7623862, 237876, 3021875 ], "anchor_spans": [ [ 35, 52 ], [ 190, 201 ], [ 648, 654 ], [ 1336, 1359 ], [ 1439, 1456 ], [ 1763, 1782 ], [ 1830, 1836 ] ] }, { "plaintext": ". ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "We now consider the two contributions separately. The polymer elastic deformation term is independent of the solvent phase and has the same expression as a rubber, as derived in the Kuhn's theory of rubber elasticity: ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 7623862 ], "anchor_spans": [ [ 199, 216 ] ] }, { "plaintext": "where denotes the shear modulus of the initial state. On the other hand, the mixing term is usually treated by the Flory-Huggins free energy of concentrated polymer solutions , where is polymer volume fraction. Suppose the initial gel has a polymer volume fraction of , the polymer volume fraction after swelling would be since the number of monomers remains the same while the gel volume has increased by a factor of . As the polymer volume fraction decreases from to , a polymer solution of concentration and volume is mixed with a pure solvent of volume to become a solution with polymer concentration and volume . The free energy density change in this mixing step is given as ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 1575447, 3010589, 53181502 ], "anchor_spans": [ [ 19, 32 ], [ 117, 142 ], [ 146, 176 ] ] }, { "plaintext": "where on the right hand side, the first term is the Flory-Huggins energy density of the final swelled gel, the second is associated with the initial gel and the third is of the pure solvent prior to mixing. Substitution of leads to ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 3010589 ], "anchor_spans": [ [ 52, 65 ] ] }, { "plaintext": ". ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Note that the second term is independent of the stretching factors , and and hence can be dropped in subsequent analysis. Now we make use of the Flory-Huggins free energy for a polymer-solvent solution that reads ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 3010589 ], "anchor_spans": [ [ 147, 160 ] ] }, { "plaintext": "where is monomer volume, is polymer strand length and is the Flory-Huggins energy parameter. Because in a network, the polymer length is effectively infinite, we can take the limit and reduces to ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 3010589 ], "anchor_spans": [ [ 64, 77 ] ] }, { "plaintext": ". ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Substitution of this expression into and addition of the network contribution leads to ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": ". ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "This provides the starting point to examining the swelling equilibrium of a gel network immersed in solvent. It can be shown that gel swelling is the competition between two forces, one is the osmotic pressure of the polymer solution that favors the take in of solvent and expansion, the other is the restoring force of the polymer network elasticity that favors shrinkage. At equilibrium, the two effects exactly cancel each other in principle and the associated , and define the equilibrium gel volume. In solving the force balance equation, graphical solutions are often preferred. ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 31383, 268923 ], "anchor_spans": [ [ 193, 209 ], [ 340, 350 ] ] }, { "plaintext": "In an alternative, scaling approach, suppose an isotropic gel is stretch by a factor of in all three directions. Under the affine network approximation, the mean-square end-to-end distance in the gel increases from initial to and the elastic energy of one stand can be written as ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 14865, 38449, 18525261 ], "anchor_spans": [ [ 48, 57 ], [ 124, 138 ], [ 170, 189 ] ] }, { "plaintext": "where is the mean-square fluctuation in end-to-end distance of one strand. The modulus of the gel is then this single-strand elastic energy multiplied by strand number density to give ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": ". ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "This modulus can then be equated to osmotic pressure (through differentiation of the free energy) to give the same equation as we found above. ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 31383 ], "anchor_spans": [ [ 36, 52 ] ] }, { "plaintext": "Consider a hydrogel made of polyelectrolytes decorated with weak acid groups that can ionize according to the reaction", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 844290, 1225002, 34251640 ], "anchor_spans": [ [ 11, 19 ], [ 28, 44 ], [ 60, 69 ] ] }, { "plaintext": "is immersed in a salt solution of physiological concentration. The degree of ionization of the polyelectrolytes is then controlled by the and due to the charged nature of and , electrostatic interactions with other ions in the systems. This is effectively a reacting system governed by acid-base equilibrium modulated by electrostatic effects, and is relevant in drug delivery, sea water desalination and dialysis technologies. Due to the elastic nature of the gel, the dispersion of in the system is constrained and hence, there will be a partitioning of salts ions and inside and outside the gel, which is intimately coupled to the polyelectrolyte degree of ionization. This ion partitioning inside and outside the gel is analogous to the partitioning of ions across a semipemerable membrane in classical Donnan theory, but a membrane is not needed here because the gel volume constraint imposed by network elasticity effectively acts its role, in preventing the macroions to pass through the fictitious membrane while allowing ions to pass. ", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 59611, 1225002, 368328, 57555, 6354378, 156787, 496264, 1225002, 6732652 ], "anchor_spans": [ [ 77, 87 ], [ 95, 111 ], [ 179, 205 ], [ 288, 309 ], [ 365, 378 ], [ 390, 402 ], [ 407, 415 ], [ 638, 653 ], [ 811, 817 ] ] }, { "plaintext": "The coupling between the ion partitioning and polyelectrolyte ionization degree is only partially by the classical Donnan theory. As a starting point we can neglect the electrostatic interactions among ions. Then at equilibrium, some of the weak acid sites in the gel would dissociate to form that electrostatically attracts positive charged and salt cations leading to a relatively high concentration of and salt cations inside the gel. But because the concentration of is locally higher, it suppresses the further ionization of the acid sites. This phenomenon is the prediction of the classical Donnan theory. However, with electrostatic interactions, there are further complications to the picture. Consider the case of two adjacent, initially uncharged acid sites are both dissociated to form . Since the two sites are both negatively charged, there will be a charge-charge repulsion along the backbone of the polymer than tends to stretch the chain. This energy cost is high both elastically and electrostatically and hence suppress ionization. Even though this ionization suppression is qualitatively similar to that of Donnan prediction, it is absent without electrostatic consideration and present irrespective of ion partitioning. The combination of both effects as well as gel elasticity determines the volume of the gel at equilibrium. Due to the complexity of the coupled acid-base equilibrium, electrostatics and network elasticity, only recently has such system been correctly recreated in computer simulations.", "section_idx": 4, "section_name": "Properties", "target_page_ids": [ 6732652, 305924 ], "anchor_spans": [ [ 115, 121 ], [ 1508, 1528 ] ] }, { "plaintext": "Some species secrete gels that are effective in parasite control. For example, the long-finned pilot whale secretes an enzymatic gel that rests on the outer surface of this animal and helps prevent other organisms from establishing colonies on the surface of these whales' bodies.", "section_idx": 5, "section_name": "Animal-produced gels", "target_page_ids": [ 372292 ], "anchor_spans": [ [ 83, 106 ] ] }, { "plaintext": "Hydrogels existing naturally in the body include mucus, the vitreous humor of the eye, cartilage, tendons and blood clots. Their viscoelastic nature results in the soft tissue component of the body, disparate from the mineral-based hard tissue of the skeletal system. Researchers are actively developing synthetically derived tissue replacement technologies derived from hydrogels, for both temporary implants (degradable) and permanent implants (non-degradable). A review article on the subject discusses the use of hydrogels for nucleus pulposus replacement, cartilage replacement, and synthetic tissue models.", "section_idx": 5, "section_name": "Animal-produced gels", "target_page_ids": [ 41207, 501188, 328850, 166945, 144865, 183058, 1910996, 210269, 307065 ], "anchor_spans": [ [ 0, 9 ], [ 49, 54 ], [ 60, 74 ], [ 87, 96 ], [ 98, 105 ], [ 110, 121 ], [ 401, 409 ], [ 531, 547 ], [ 588, 604 ] ] }, { "plaintext": "Many substances can form gels when a suitable thickener or gelling agent is added to their formula. This approach is common in manufacture of wide range of products, from foods to paints and adhesives.", "section_idx": 6, "section_name": "Applications", "target_page_ids": [ 2518458 ], "anchor_spans": [ [ 46, 72 ] ] }, { "plaintext": "In fiber optic communications, a soft gel resembling hair gel in viscosity is used to fill the plastic tubes containing the fibers. The main purpose of the gel is to prevent water intrusion if the buffer tube is breached, but the gel also buffers the fibers against mechanical damage when the tube is bent around corners during installation, or flexed. Additionally, the gel acts as a processing aid when the cable is being constructed, keeping the fibers central whilst the tube material is extruded around it.", "section_idx": 6, "section_name": "Applications", "target_page_ids": [ 908000 ], "anchor_spans": [ [ 53, 61 ] ] }, { "plaintext": " Aerogel", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 50069638 ], "anchor_spans": [ [ 1, 8 ] ] }, { "plaintext": " 2-Acrylamido-2-methylpropane sulfonic acid", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 22439870 ], "anchor_spans": [ [ 1, 43 ] ] }, { "plaintext": " Agarose gel electrophoresis", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 1910 ], "anchor_spans": [ [ 1, 28 ] ] }, { "plaintext": " Food rheology", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 24391644 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Gel electrophoresis", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 12582 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": " Gel filtration chromatography", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 97911 ], "anchor_spans": [ [ 1, 30 ] ] }, { "plaintext": " Gel pack", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 2420839 ], "anchor_spans": [ [ 1, 9 ] ] }, { "plaintext": " Gel permeation chromatography", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 345286 ], "anchor_spans": [ [ 1, 30 ] ] }, { "plaintext": " Hydrocolloid", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 5346 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Ouchterlony double immunodiffusion", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 4948339 ], "anchor_spans": [ [ 1, 35 ] ] }, { "plaintext": " Paste (rheology)", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 922972 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Polyacrylamide gel electrophoresis", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 102352 ], "anchor_spans": [ [ 1, 35 ] ] }, { "plaintext": " Radial immunodiffusion", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 11759876 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Silicone gel", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 65827 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Two-dimensional gel electrophoresis", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 474372 ], "anchor_spans": [ [ 1, 36 ] ] }, { "plaintext": " Void (composites)", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 44578263 ], "anchor_spans": [ [ 1, 18 ] ] } ]

[ "Articles_containing_video_clips", "Colloids", "Dosage_forms", "Drug_delivery_devices", "Gels", "Physical_chemistry" ]

[]

[ { "plaintext": "A geostationary orbit, also referred to as a geosynchronous equatorial orbit (GEO), is a circular geosynchronous orbit in altitude above Earth's Equator ( in radius from Earth's center) and following the direction of Earth's rotation.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 997205, 40239, 20611356, 23994165, 4396171 ], "anchor_spans": [ [ 89, 97 ], [ 98, 118 ], [ 146, 153 ], [ 205, 214 ], [ 218, 234 ] ] }, { "plaintext": "An object in such an orbit has an orbital period equal to Earth's rotational period, one sidereal day, and so to ground observers it appears motionless, in a fixed position in the sky. The concept of a geostationary orbit was popularised by the science fiction writer Arthur C. Clarke in the 1940s as a way to revolutionise telecommunications, and the first satellite to be placed in this kind of orbit was launched in 1963.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 143696, 48837, 18598148, 27683 ], "anchor_spans": [ [ 34, 48 ], [ 89, 101 ], [ 268, 284 ], [ 358, 367 ] ] }, { "plaintext": "Communications satellites are often placed in a geostationary orbit so that Earth-based satellite antennas (located on Earth) do not have to rotate to track them but can be pointed permanently at the position in the sky where the satellites are located. Weather satellites are also placed in this orbit for real-time monitoring and data collection, and navigation satellites to provide a known calibration point and enhance GPS accuracy.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 45207, 192615, 264727, 1515653 ], "anchor_spans": [ [ 0, 24 ], [ 88, 106 ], [ 254, 271 ], [ 353, 374 ] ] }, { "plaintext": "Geostationary satellites are launched via a temporary orbit, and placed in a slot above a particular point on the Earth's surface. The orbit requires some stationkeeping to keep its position, and modern retired satellites are placed in a higher graveyard orbit to avoid collisions.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 11962478, 1244926 ], "anchor_spans": [ [ 44, 59 ], [ 245, 260 ] ] }, { "plaintext": "In 1929, Herman Potočnik described both geosynchronous orbits in general and the special case of the geostationary Earth orbit in particular as useful orbits for space stations. The first appearance of a geostationary orbit in popular literature was in October 1942, in the first Venus Equilateral story by George O. Smith, but Smith did not go into details. British science fiction author Arthur C. Clarke popularised and expanded the concept in a 1945 paper entitled Extra-Terrestrial Relays – Can Rocket Stations Give Worldwide Radio Coverage?, published in Wireless World magazine. Clarke acknowledged the connection in his introduction to The Complete Venus Equilateral. The orbit, which Clarke first described as useful for broadcast and relay communications satellites, is sometimes called the Clarke Orbit. Similarly, the collection of artificial satellites in this orbit is known as the Clarke Belt.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 86634, 50896, 22498, 6958163, 384038, 26787, 18598148, 24053883 ], "anchor_spans": [ [ 9, 24 ], [ 162, 175 ], [ 218, 223 ], [ 280, 297 ], [ 307, 322 ], [ 367, 382 ], [ 390, 406 ], [ 561, 575 ] ] }, { "plaintext": "In technical terminology the orbit is referred to as either a geostationary or geosynchronous equatorial orbit, with the terms used somewhat interchangeably.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The first geostationary satellite was designed by Harold Rosen while he was working at Hughes Aircraft in 1959. Inspired by Sputnik 1, he wanted to use a geostationary satellite to globalise communications. Telecommunications between the US and Europe was then possible between just 136 people at a time, and reliant on high frequency radios and an undersea cable.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 10150062, 335475, 28484, 178937, 45206 ], "anchor_spans": [ [ 50, 62 ], [ 87, 102 ], [ 124, 133 ], [ 320, 334 ], [ 349, 363 ] ] }, { "plaintext": "Conventional wisdom at the time was that it would require too much rocket power to place a satellite in a geostationary orbit and it would not survive long enough to justify the expense, so early efforts were put towards constellations of satellites in low or medium Earth orbit. The first of these were the passive Echo balloon satellites in 1960, followed by Telstar 1 in 1962. Although these projects had difficulties with signal strength and tracking, that could be solved through geostationary satellites, the concept was seen as impractical, so Hughes often withheld funds and support.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 26301, 47568, 6696241, 948738, 425262 ], "anchor_spans": [ [ 67, 73 ], [ 253, 256 ], [ 260, 266 ], [ 316, 339 ], [ 361, 370 ] ] }, { "plaintext": "By 1961, Rosen and his team had produced a cylindrical prototype with a diameter of , height of , weighing , light and small enough to be placed into orbit. It was spin stabilised with a dipole antenna producing a pancake shaped waveform. In August 1961, they were contracted to begin building the real satellite. They lost Syncom 1 to electronics failure, but Syncom 2 was successfully placed into a geosynchronous orbit in 1963. Although its inclined orbit still required moving antennas, it was able to relay TV transmissions, and allowed for US President John F. Kennedy to phone Nigerian prime minister Abubakar Tafawa Balewa from a ship on August 23, 1963.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 2306393, 92138, 92138, 345848, 5119376, 674763 ], "anchor_spans": [ [ 164, 179 ], [ 324, 332 ], [ 361, 369 ], [ 444, 458 ], [ 559, 574 ], [ 608, 630 ] ] }, { "plaintext": "The first satellite placed in a geostationary orbit was Syncom 3, which was launched by a Delta D rocket in 1964. With its increased bandwidth, this satellite was able to transmit live coverage of the Summer Olympics from Japan to America. Geostationary orbits have been in common use ever since, in particular for satellite television.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 92138, 423056 ], "anchor_spans": [ [ 56, 64 ], [ 90, 104 ] ] }, { "plaintext": "Today there are hundreds of geostationary satellites providing remote sensing and communications.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Although most populated land locations on the planet now have terrestrial communications facilities (microwave, fiber-optic), with telephone access covering 96% of the population and internet access 90%, some rural and remote areas in developed countries are still reliant on satellite communications.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 20097, 3372377 ], "anchor_spans": [ [ 101, 110 ], [ 112, 123 ] ] }, { "plaintext": "Most commercial communications satellites, broadcast satellites and SBAS satellites operate in geostationary orbits.", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 45207, 1040128, 8441903 ], "anchor_spans": [ [ 16, 40 ], [ 43, 62 ], [ 68, 72 ] ] }, { "plaintext": "Geostationary communication satellites are useful because they are visible from a large area of the earth's surface, extending 81° away in both latitude and longitude. They appear stationary in the sky, which eliminates the need for ground stations to have movable antennas. This means that Earth-based observers can erect small, cheap and stationary antennas that are always directed at the desired satellite. However, latency becomes significant as it takes about 240ms for a signal to pass from a ground based transmitter on the equator to the satellite and back again. This delay presents problems for latency-sensitive applications such as voice communication, so geostationary communication satellites are primarily used for unidirectional entertainment and applications where low latency alternatives are not available.", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 17933 ], "anchor_spans": [ [ 420, 427 ] ] }, { "plaintext": "Geostationary satellites are directly overhead at the equator and appear lower in the sky to an observer nearer the poles. As the observer's latitude increases, communication becomes more difficult due to factors such as atmospheric refraction, Earth's thermal emission, line-of-sight obstructions, and signal reflections from the ground or nearby structures. At latitudes above about 81°, geostationary satellites are below the horizon and cannot be seen at all. Because of this, some Russian communication satellites have used elliptical Molniya and Tundra orbits, which have excellent visibility at high latitudes.", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 1784072, 185239, 25391, 997097, 616351, 4662630 ], "anchor_spans": [ [ 221, 243 ], [ 253, 269 ], [ 486, 492 ], [ 529, 539 ], [ 540, 547 ], [ 552, 558 ] ] }, { "plaintext": "A worldwide network of operational geostationary meteorological satellites is used to provide visible and infrared images of Earth's surface and atmosphere for weather observation, oceanography, and atmospheric tracking. As of 2019 there are 19 satellites in either operation or stand-by. These satellite systems include:", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 264727, 241913, 44044 ], "anchor_spans": [ [ 35, 73 ], [ 106, 121 ], [ 181, 193 ] ] }, { "plaintext": " the United States' GOES series, operated by NOAA", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 82915, 37876 ], "anchor_spans": [ [ 20, 24 ], [ 45, 49 ] ] }, { "plaintext": " the Meteosat series, launched by the European Space Agency and operated by the European Weather Satellite Organization, EUMETSAT", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 746612, 10363, 610000 ], "anchor_spans": [ [ 5, 13 ], [ 38, 59 ], [ 121, 129 ] ] }, { "plaintext": " the Republic of Korea COMS-1 and GK-2A multi mission satellites.", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 27857123 ], "anchor_spans": [ [ 23, 29 ] ] }, { "plaintext": " the Russian Elektro-L satellites", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 30581385 ], "anchor_spans": [ [ 13, 22 ] ] }, { "plaintext": " the Japanese Himawari series", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 19181851 ], "anchor_spans": [ [ 14, 22 ] ] }, { "plaintext": " Chinese Fengyun series", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 3743846 ], "anchor_spans": [ [ 9, 16 ] ] }, { "plaintext": " India's INSAT series", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 633244 ], "anchor_spans": [ [ 9, 14 ] ] }, { "plaintext": "These satellites typically captures images in the visual and infrared spectrum with a spatial resolution between 0.5 and 4 square kilometres. The coverage is typically 70°, and in some cases less.", "section_idx": 2, "section_name": "Uses", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Geostationary satellite imagery has been used for tracking volcanic ash, measuring cloud top temperatures and water vapour, oceanography, measuring land temperature and vegetation coverage, facilitating cyclone path prediction, and providing real time cloud coverage and other tracking data. Some information has been incorporated into meteorological prediction models, but due to their wide field of view, full-time monitoring and lower resolution, geostationary weather satellite images are primarily used for short-term and real-time forecasting.", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 47863556, 35845586, 42806, 1505381 ], "anchor_spans": [ [ 59, 71 ], [ 124, 136 ], [ 203, 210 ], [ 336, 368 ] ] }, { "plaintext": "Geostationary satellites can be used to augment GNSS systems by relaying clock, ephemeris and ionospheric error corrections (calculated from ground stations of a known position) and providing an additional reference signal. This improves position accuracy from approximately 5m to 1m or less.", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 1515653, 27616141, 27616141, 27616141 ], "anchor_spans": [ [ 48, 52 ], [ 73, 78 ], [ 80, 89 ], [ 94, 105 ] ] }, { "plaintext": "Past and current navigation systems that use geostationary satellites include:", "section_idx": 2, "section_name": "Uses", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " The Wide Area Augmentation System (WAAS), operated by the United States Federal Aviation Administration (FAA);", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 862061, 3434750, 11186 ], "anchor_spans": [ [ 5, 34 ], [ 59, 72 ], [ 73, 104 ] ] }, { "plaintext": " The European Geostationary Navigation Overlay Service (EGNOS), operated by the ESSP (on behalf of EU's GSA);", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 199645, 9317, 57699817 ], "anchor_spans": [ [ 5, 54 ], [ 99, 101 ], [ 104, 107 ] ] }, { "plaintext": " The Multi-functional Satellite Augmentation System (MSAS), operated by Japan's Ministry of Land, Infrastructure and Transport Japan Civil Aviation Bureau (JCAB);", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 6855695, 15573, 1327991, 41510220 ], "anchor_spans": [ [ 5, 51 ], [ 72, 77 ], [ 80, 126 ], [ 127, 154 ] ] }, { "plaintext": " The GPS Aided Geo Augmented Navigation (GAGAN) system being operated by India.", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 8231648, 14533 ], "anchor_spans": [ [ 5, 39 ], [ 73, 78 ] ] }, { "plaintext": " The commercial StarFire navigation system, operated by John Deere and C-Nav Positioning Solutions (Oceaneering);", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 5559303, 432397, 16933230 ], "anchor_spans": [ [ 16, 42 ], [ 56, 66 ], [ 100, 111 ] ] }, { "plaintext": " The commercial Starfix DGPS System and OmniSTAR system, operated by Fugro.", "section_idx": 2, "section_name": "Uses", "target_page_ids": [ 15219400, 12337865 ], "anchor_spans": [ [ 40, 48 ], [ 69, 74 ] ] }, { "plaintext": "Geostationary satellites are launched to the east into a prograde orbit that matches the rotation rate of the equator. The smallest inclination that a satellite can be launched into is that of the launch site's latitude, so launching the satellite from close to the equator limits the amount of inclination change needed later. Additionally, launching from close to the equator allows the speed of the Earth's rotation to give the satellite a boost. A launch site should have water or deserts to the east, so any failed rockets do not fall on a populated area.", "section_idx": 3, "section_name": "Implementation", "target_page_ids": [ 979374 ], "anchor_spans": [ [ 295, 313 ] ] }, { "plaintext": "Most launch vehicles place geostationary satellites directly into a geostationary transfer orbit (GTO), an elliptical orbit with an apogee at GEO height and a low perigee. On-board satellite propulsion is then used to raise the perigee, circularise and reach GEO.", "section_idx": 3, "section_name": "Implementation", "target_page_ids": [ 1306157, 178282, 88213, 88213 ], "anchor_spans": [ [ 5, 19 ], [ 68, 96 ], [ 132, 138 ], [ 163, 170 ] ] }, { "plaintext": "Satellites in geostationary orbit must all occupy a single ring above the equator. The requirement to space these satellites apart, to avoid harmful radio-frequency interference during operations, means that there are a limited number of orbital slots available, and thus only a limited number of satellites can be operated in geostationary orbit. This has led to conflict between different countries wishing access to the same orbital slots (countries near the same longitude but differing latitudes) and radio frequencies. These disputes are addressed through the International Telecommunication Union's allocation mechanism under the Radio Regulations. In the 1976 Bogota Declaration, eight countries located on the Earth's equator claimed sovereignty over the geostationary orbits above their territory, but the claims gained no international recognition.", "section_idx": 3, "section_name": "Implementation", "target_page_ids": [ 20611356, 17617, 17616, 42852, 14836, 131442, 30578787 ], "anchor_spans": [ [ 74, 81 ], [ 467, 476 ], [ 491, 500 ], [ 506, 523 ], [ 566, 603 ], [ 637, 654 ], [ 668, 686 ] ] }, { "plaintext": "A statite is a hypothetical satellite that uses radiation pressure from the sun against a solar sail to modify its orbit.", "section_idx": 3, "section_name": "Implementation", "target_page_ids": [ 29417, 43709, 29420 ], "anchor_spans": [ [ 2, 9 ], [ 48, 66 ], [ 90, 100 ] ] }, { "plaintext": "It would hold its location over the dark side of the Earth at a latitude of approximately 30 degrees. A statite is stationary relative to the Earth and Sun system rather than compared to surface of the Earth, and could ease congestion in the geostationary ring.", "section_idx": 3, "section_name": "Implementation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Geostationary satellites require some station keeping to keep their position, and once they run out of thruster fuel they are generally retired. The transponders and other onboard systems often outlive the thruster fuel and by allowing the satellite to move naturally into an inclined geosynchronous orbit some satellites can remain in use, or else be elevated to a graveyard orbit. This process is becoming increasingly regulated and satellites must have a 90% chance of moving over 200km above the geostationary belt at end of life.", "section_idx": 4, "section_name": "Retired satellites", "target_page_ids": [ 41210, 979306, 13442133, 1244926 ], "anchor_spans": [ [ 0, 23 ], [ 38, 53 ], [ 149, 161 ], [ 366, 381 ] ] }, { "plaintext": "Space debris at geostationary orbits typically has a lower collision speed than at LEO since all GEO satellites orbit in the same plane, altitude and speed; however, the presence of satellites in eccentric orbits allows for collisions at up to 4km/s. Although a collision is comparatively unlikely, GEO satellites have a limited ability to avoid any debris.", "section_idx": 4, "section_name": "Retired satellites", "target_page_ids": [ 1099413 ], "anchor_spans": [ [ 196, 212 ] ] }, { "plaintext": "Debris less than 10cm in diameter cannot be seen from the Earth, making it difficult to assess their prevalence.", "section_idx": 4, "section_name": "Retired satellites", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Despite efforts to reduce risk, spacecraft collisions have occurred. The European Space Agency telecom satellite Olympus-1 was struck by a meteoroid on August 11, 1993 and eventually moved to a graveyard orbit, and in 2006 the Russian Express-AM11 communications satellite was struck by an unknown object and rendered inoperable, although its engineers had enough contact time with the satellite to send it into a graveyard orbit. In 2017, both AMC-9 and Telkom-1 broke apart from an unknown cause.", "section_idx": 4, "section_name": "Retired satellites", "target_page_ids": [ 10363, 32457315, 63793, 1244926, 7105106, 51218802, 67528686 ], "anchor_spans": [ [ 73, 94 ], [ 113, 122 ], [ 139, 148 ], [ 194, 209 ], [ 235, 247 ], [ 445, 450 ], [ 455, 463 ] ] }, { "plaintext": "A typical geostationary orbit has the following properties:", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Inclination: 0°", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Period: 1436 minutes (one sidereal day)", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 48837 ], "anchor_spans": [ [ 27, 39 ] ] }, { "plaintext": " Eccentricity: 0", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Argument of perigee: undefined", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Semi-major axis: 42,164km", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 23409699 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": "An inclination of zero ensures that the orbit remains over the equator at all times, making it stationary with respect to latitude from the point of view of a ground observer (and in the Earth-centered Earth-fixed reference frame).", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 5644032 ], "anchor_spans": [ [ 187, 213 ] ] }, { "plaintext": "The orbital period is equal to exactly one sidereal day. This means that the satellite will return to the same point above the Earth's surface every (sidereal) day, regardless of other orbital properties. For a geostationary orbit in particular, it ensures that it holds the same longitude over time. This orbital period, T, is directly related to the semi-major axis of the orbit through the formula:", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where:", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the length of the orbit's semi-major axis", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the standard gravitational parameter of the central body", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 996808 ], "anchor_spans": [ [ 9, 41 ] ] }, { "plaintext": "The eccentricity is zero, which produces a circular orbit. This ensures that the satellite does not move closer or further away from the Earth, which would cause it to track backwards and forwards across the sky.", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 997205 ], "anchor_spans": [ [ 43, 57 ] ] }, { "plaintext": "A geostationary orbit can be achieved only at an altitude very close to and directly above the equator. This equates to an orbital speed of and an orbital period of 1,436 minutes, one sidereal day. This ensures that the satellite will match the Earth's rotational period and has a stationary footprint on the ground. All geostationary satellites have to be located on this ring.", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 48837, 841262 ], "anchor_spans": [ [ 186, 198 ], [ 294, 303 ] ] }, { "plaintext": "A combination of lunar gravity, solar gravity, and the flattening of the Earth at its poles causes a precession motion of the orbital plane of any geostationary object, with an orbital period of about 53 years and an initial inclination gradient of about 0.85° per year, achieving a maximal inclination of 15° after 26.5 years. To correct for this perturbation, regular orbital stationkeeping maneuvers are necessary, amounting to a delta-v of approximately 50m/s per year.", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 19331, 26751, 143023, 24714, 143696, 1490148, 979306, 194465 ], "anchor_spans": [ [ 17, 22 ], [ 32, 37 ], [ 55, 78 ], [ 101, 111 ], [ 177, 191 ], [ 348, 360 ], [ 370, 392 ], [ 433, 440 ] ] }, { "plaintext": "A second effect to be taken into account is the longitudinal drift, caused by the asymmetry of the Earth – the equator is slightly elliptical. There are two stable equilibrium points (at 75.3°E and 108°W) and two corresponding unstable points (at 165.3°E and 14.7°W). Any geostationary object placed between the equilibrium points would (without any action) be slowly accelerated towards the stable equilibrium position, causing a periodic longitude variation. The correction of this effect requires station-keeping maneuvers with a maximal delta-v of about 2m/s per year, depending on the desired longitude.", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 979306 ], "anchor_spans": [ [ 500, 525 ] ] }, { "plaintext": "Solar wind and radiation pressure also exert small forces on satellites: over time, these cause them to slowly drift away from their prescribed orbits.", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 28538, 43709 ], "anchor_spans": [ [ 0, 10 ], [ 15, 33 ] ] }, { "plaintext": "In the absence of servicing missions from the Earth or a renewable propulsion method, the consumption of thruster propellant for station-keeping places a limitation on the lifetime of the satellite. Hall-effect thrusters, which are currently in use, have the potential to prolong the service life of a satellite by providing high-efficiency electric propulsion.", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 37838, 6650279 ], "anchor_spans": [ [ 199, 219 ], [ 341, 360 ] ] }, { "plaintext": "For circular orbits around a body, the centripetal force required to maintain the orbit (Fc) is equal to the gravitational force acting on the satellite (Fg):", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 7534 ], "anchor_spans": [ [ 39, 56 ] ] }, { "plaintext": "From Isaac Newton's Universal law of gravitation,", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 14627, 244611 ], "anchor_spans": [ [ 5, 17 ], [ 20, 48 ] ] }, { "plaintext": ",", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where Fg is the gravitational force acting between two objects, ME is the mass of the Earth, , ms is the mass of the satellite, r is the distance between the centers of their masses, and G is the gravitational constant, .", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 173961, 38454 ], "anchor_spans": [ [ 158, 181 ], [ 196, 218 ] ] }, { "plaintext": "The magnitude of the acceleration, a, of a body moving in a circle is given by:", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where v is the magnitude of the velocity (i.e. the speed) of the satellite. From Newton's Second law of Motion, the centripetal force Fc is given by:", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 20491903, 55212 ], "anchor_spans": [ [ 32, 40 ], [ 81, 110 ] ] }, { "plaintext": ".", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "As Fc = Fg,", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": ",", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "so that", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Replacing v with the equation for the speed of an object moving around a circle produces:", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 574544 ], "anchor_spans": [ [ 38, 79 ] ] }, { "plaintext": "where T is the orbital period (i.e. one sidereal day), and is equal to . This gives an equation for r:", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The product GME is known with much greater precision than either factor alone; it is known as the geocentric gravitational constant μ = . Hence", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 996808 ], "anchor_spans": [ [ 98, 131 ] ] }, { "plaintext": "The resulting orbital radius is . Subtracting the Earth's equatorial radius, , gives the altitude of .", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 146689 ], "anchor_spans": [ [ 50, 75 ] ] }, { "plaintext": "The orbital speed is calculated by multiplying the angular speed by the orbital radius:", "section_idx": 5, "section_name": "Properties", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "By the same method, we can determine the orbital altitude for any similar pair of bodies, including the areostationary orbit of an object in relation to Mars, if it is assumed that it is spherical (which it is not entirely). The gravitational constant GM (μ) for Mars has the value of , its equatorial radius is and the known rotational period (T) of the planet is (). Using these values, Mars' orbital altitude is equal to .", "section_idx": 5, "section_name": "Properties", "target_page_ids": [ 997141, 14640471, 996808, 743909 ], "anchor_spans": [ [ 104, 124 ], [ 153, 157 ], [ 229, 251 ], [ 327, 344 ] ] }, { "plaintext": " List of orbits", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 9622293 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " List of satellites in geosynchronous orbit", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 1040128 ], "anchor_spans": [ [ 1, 43 ] ] }, { "plaintext": " Orbital station-keeping", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 979306 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Space elevator, which ultimately reaches a geostationary orbit", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 29192 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " How to get a satellite to geostationary orbit", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Orbital Mechanics (Rocket and Space Technology)", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " List of satellites in geostationary orbit", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Clarke Belt Snapshot Calculator", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " 3D Real Time Satellite Tracking", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Geostationary satellite orbit overview", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Daily animation of the Earth, made by geostationary satellite 'Electro L' photos Satellite shoots 48 images of the planet every day.", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Orbital Mechanics for Engineering Students", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Astrodynamics", "Earth_orbits", "Satellites_in_geostationary_orbit" ]

[ "geostationary Earth orbit", "geosynchronous equatorial orbit", "GEO" ]

[ { "plaintext": "A graded-index or gradient-index fiber is an optical fiber whose core has a refractive index that decreases with increasing radial distance from the optical axis of the fiber.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 3372377, 3372377, 25880, 41456 ], "anchor_spans": [ [ 45, 58 ], [ 65, 69 ], [ 76, 92 ], [ 149, 161 ] ] }, { "plaintext": "Because parts of the core closer to the fiber axis have a higher refractive index than the parts near the cladding, light rays follow sinusoidal paths down the fiber. The most common refractive index profile for a graded-index fiber is very nearly parabolic. The parabolic profile results in continual refocusing of the rays in the core, and minimizes modal dispersion.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 324749, 23231, 7705960 ], "anchor_spans": [ [ 134, 144 ], [ 263, 272 ], [ 352, 368 ] ] }, { "plaintext": "Multi-mode optical fiber can be built with either graded index or step index. The advantage of the multi-mode graded index compared to the multi-mode step index is the considerable decrease in modal dispersion. Modal dispersion can be further decreased by selecting a smaller core size (less than 5–10μm) and forming a single-mode step index fiber.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 2940457, 41748, 41716 ], "anchor_spans": [ [ 0, 24 ], [ 66, 76 ], [ 319, 347 ] ] }, { "plaintext": "This type of fiber is normalized by the International Telecommunication Union ITU-T at recommendation G.651.1.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Pulse dispersion in a graded index optical fiber is given by", "section_idx": 1, "section_name": "Pulse dispersion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where", "section_idx": 1, "section_name": "Pulse dispersion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the difference in refractive indices of core and cladding,", "section_idx": 1, "section_name": "Pulse dispersion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the refractive index of the cladding,", "section_idx": 1, "section_name": "Pulse dispersion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the length of the fiber taken for observing the pulse dispersion,", "section_idx": 1, "section_name": "Pulse dispersion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is the speed of light, and", "section_idx": 1, "section_name": "Pulse dispersion", "target_page_ids": [ 28736 ], "anchor_spans": [ [ 8, 22 ] ] }, { "plaintext": " is the constant of graded index profile.", "section_idx": 1, "section_name": "Pulse dispersion", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Power-law index profile", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 41570 ], "anchor_spans": [ [ 0, 23 ] ] }, { "plaintext": "Gradient index optics", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 663580 ], "anchor_spans": [ [ 0, 21 ] ] } ]

[ "Optical_fiber" ]

[]

[ { "plaintext": "In telecommunication engineering, and in particular teletraffic engineering, the quality of voice service is specified by two measures: the grade of service (GoS) and the quality of service (QoS).", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 1536216, 25315 ], "anchor_spans": [ [ 3, 20 ], [ 52, 75 ], [ 171, 189 ] ] }, { "plaintext": "Grade of service is the probability of a call in a circuit group being blocked or delayed for more than a specified interval, expressed as a vulgar fraction or decimal fraction. This is always with reference to the busy hour when the traffic intensity is the greatest. Grade of service may be viewed independently from the perspective of incoming versus outgoing calls, and is not necessarily equal in each direction or between different source-destination pairs. \"Grade of Service\" sometimes means a measure of inbound call center traffic to verify adherence to conditions to measure the success of customers served.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 22934, 406703, 1704824, 8214, 6968491, 43081, 7243 ], "anchor_spans": [ [ 24, 35 ], [ 41, 45 ], [ 141, 156 ], [ 160, 176 ], [ 215, 224 ], [ 234, 241 ], [ 521, 532 ] ] }, { "plaintext": "On the other hand, the quality of service which a single circuit is designed or conditioned to provide, e.g. voice grade or program grade is called the quality of service. Quality criteria for such circuits may include equalization for amplitude over a specified band of frequencies, or in the case of digital data transported via analogue circuits, may include equalization for phase. Criteria for mobile quality of service in cellular telephone circuits include the probability of abnormal termination of the call.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 346001, 26332696, 634183, 8276, 24047, 1560803 ], "anchor_spans": [ [ 57, 64 ], [ 219, 231 ], [ 263, 267 ], [ 302, 314 ], [ 379, 384 ], [ 399, 424 ] ] }, { "plaintext": "When a user attempts to make a telephone call, the routing equipment handling the call has to determine whether to accept the call, reroute the call to alternative equipment, or reject the call entirely. Rejected calls occur as a result of heavy traffic loads (congestion) on the system and can result in the call either being delayed or lost. If a call is delayed, the user simply has to wait for the traffic to decrease, however if a call is lost then it is removed from the system.", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The Grade of Service is one aspect of the quality a customer can expect to experience when making a telephone call. In a Loss System, the Grade of Service is described as that proportion of calls that are lost due to congestion in the busy hour. ", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [ 25315 ], "anchor_spans": [ [ 42, 49 ] ] }, { "plaintext": "For a Lost Call system, the Grade of Service can be measured using Equation 1. ", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For a delayed call system, the Grade of Service is measured using three separate terms:", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The mean delay Describes the average time a user spends waiting for a connection if their call is delayed.", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The mean delay Describes the average time a user spends waiting for a connection whether or not their call is delayed.", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The probability that a user may be delayed longer than time t while waiting for a connection. Time t is chosen by the telecommunications service provider so that they can measure whether their services conform to a set Grade of Service.", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Where and when is Grade of Service measured?", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The Grade of Service can be measured using different sections of a network. When a call is routed from one end to another, it will pass through several exchanges. If the Grade of Service is calculated based on the number of calls rejected by the final circuit group, then the Grade of Service is determined by the final circuit group blocking criteria. If the Grade of Service is calculated based on the number of rejected calls between exchanges, then the Grade of Service is determined by the exchange-to-exchange blocking criteria.", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The Grade of Service should be calculated using both the access networks and the core networks as it is these networks that allow a user to complete an end-to-end connection. Furthermore, the Grade of Service should be calculated from the average of the busy hour traffic intensities of the 30 busiest traffic days of the year. This will cater for most scenarios as the traffic intensity will seldom exceed the reference level.", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The grade of service is a measure of the ability of a user to access a trunk system during the busiest hour. The busy is based upon customer demand at the busiest hour during a week month or year.", "section_idx": 1, "section_name": "What is Grade of Service and how is it measured?", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Different telecommunications applications require different Qualities of Service. For example, if a telecommunications service provider decides to offer different qualities of voice connection, then a premium voice connection will require a better connection quality compared to an ordinary voice connection. Thus different Qualities of Service are appropriate, depending on the intended use. To help telecommunications service providers to market their different services, each service is placed into a specific class. Each Class of Service determines the level of service required.", "section_idx": 2, "section_name": "Class of Service", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "To identify the Class of Service for a specific service, the network’s switches and routers examine the call based on several factors. Such factors can include:", "section_idx": 2, "section_name": "Class of Service", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The type of service and priority due to precedence", "section_idx": 2, "section_name": "Class of Service", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The identity of the initiating party", "section_idx": 2, "section_name": "Class of Service", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The identity of the recipient party", "section_idx": 2, "section_name": "Class of Service", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In broadband networks, the Quality of Service is measured using two criteria. The first criterion is the probability of packet losses or delays in already accepted calls. The second criterion refers to the probability that a new incoming call will be rejected or blocked. To avoid the former, broadband networks limit the number of active calls so that packets from established calls will not be lost due to new calls arriving. As in circuit-switched networks, the Grade of Service can be calculated for individual switches or for the whole network.", "section_idx": 3, "section_name": "Quality of Service in broadband networks", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The telecommunications provider is usually aware of the required Grade of Service for a particular product. To achieve and maintain a given Grade of Service, the operator must ensure that sufficient telecommunications circuits or routes are available to meet a specific level of demand. It should also be kept in mind that too many circuits will create a situation where the operator is providing excess capacity which may never be used, or at the very least may be severely underutilized. This adds costs which must be borne by other parts of the network. To determine the correct number of circuits that are required, telecommunications service providers make use of Traffic Tables. An example of a Traffic Table can be viewed in Figure 1. It follows that in order for a telecommunications network to continue to offer a given Grade of Service, the number of circuits provided in a circuit group must increase (non-linearly) if the traffic intensity increases.", "section_idx": 4, "section_name": "Maintaining a Grade of Service", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "To calculate the Grade of Service of a specified group of circuits or routes, Agner Krarup Erlang used a set of assumptions that relied on the network losing calls when all circuits in a group were busy. These assumptions are:", "section_idx": 5, "section_name": "Erlang's lost call assumptions", "target_page_ids": [ 2948 ], "anchor_spans": [ [ 78, 97 ] ] }, { "plaintext": "All traffic through the network is pure-chance traffic, i.e. all call arrivals and terminations are independent random events", "section_idx": 5, "section_name": "Erlang's lost call assumptions", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "There is statistical equilibrium, i.e., the average number of calls does not change", "section_idx": 5, "section_name": "Erlang's lost call assumptions", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Full availability of the network, i.e., every outlet from a switch is accessible from every inlet", "section_idx": 5, "section_name": "Erlang's lost call assumptions", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Any call that encounters congestion is immediately lost.", "section_idx": 5, "section_name": "Erlang's lost call assumptions", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "From these assumptions Erlang developed the Erlang-B formula which describes the probability of congestion in a circuit group. The probability of congestion gives the Grade of Service experienced.", "section_idx": 5, "section_name": "Erlang's lost call assumptions", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "To determine the Grade of Service of a network when the traffic load and number of circuits are known, telecommunications network operators make use of Equation 2, which is the Erlang-B equation. ", "section_idx": 6, "section_name": "Calculating the Grade of Service", "target_page_ids": [ 10283 ], "anchor_spans": [ [ 178, 186 ] ] }, { "plaintext": "A = Expected traffic intensity in Erlangs,", "section_idx": 6, "section_name": "Calculating the Grade of Service", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "N = Number of circuits in group.", "section_idx": 6, "section_name": "Calculating the Grade of Service", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "This equation allows operators to determine whether each of their circuit groups meet the required Grade of Service, simply by monitoring the reference traffic intensity. ", "section_idx": 6, "section_name": "Calculating the Grade of Service", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "(For delay networks, the Erlang-C formula allows network operators to determine the probability of delay depending on peak traffic and the number of circuits.)", "section_idx": 6, "section_name": "Calculating the Grade of Service", "target_page_ids": [ 199028 ], "anchor_spans": [ [ 25, 33 ] ] } ]

[ "Telecommunications_engineering", "Teletraffic" ]

[]

[ { "plaintext": "In ISO/IEC 646 (commonly known as ASCII) and related standards including ISO 8859 and Unicode, a graphic character is any character intended to be written, printed, or otherwise displayed in a form that can be read by humans. In other words, it is any encoded character that is associated with one or more glyphs.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 193891, 586, 15020, 31742, 5295, 12904 ], "anchor_spans": [ [ 3, 14 ], [ 34, 39 ], [ 73, 81 ], [ 86, 93 ], [ 252, 269 ], [ 306, 311 ] ] }, { "plaintext": "In ISO 646, graphic characters are contained in rows 2 through 7 of the code table. However, two of the characters in these rows, namely the space character SP at row 2 column 0 and the delete characterDEL (also called the rubout character) at row 7 column 15, require special mention.", "section_idx": 1, "section_name": "ISO/IEC 646", "target_page_ids": [ 5225, 2956700, 10390862 ], "anchor_spans": [ [ 72, 76 ], [ 141, 156 ], [ 186, 202 ] ] }, { "plaintext": "The space is considered to be both a graphic character and a control character in ISO 646. It can have a visible form, and also a control function (moving the print head).", "section_idx": 1, "section_name": "ISO/IEC 646", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The delete character is strictly a control character, not a graphic character. This is true not only in ISO 646, but also in all related standards including Unicode. However, many modern character sets deviate from ISO 646, and as a result a graphic character might occupy the position originally reserved for the delete character.", "section_idx": 1, "section_name": "ISO/IEC 646", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In Unicode, Graphic characters are those with General Category Letter, Mark, Number, Punctuation, Symbol or Zs=space. Other code points (General categories Control, Zl=line separator, Zp=paragraph separator) are Format, Control, Private Use, Surrogate, Noncharacter or Reserved (unassigned).", "section_idx": 2, "section_name": "Unicode", "target_page_ids": [ 27344287 ], "anchor_spans": [ [ 46, 62 ] ] }, { "plaintext": "Most graphic characters are spacing characters, which means that each instance of a spacing character has to occupy some area in a graphic representation. For a teletype or a typewriter this implies moving of the carriage after typing of a character. In the context of text mode display, each spacing character occupies one rectangular character box of equal sizes. Or maybe two adjacent ones, for non-alphabetic characters of East Asian languages. If a text is rendered using proportional fonts, widths of character boxes are not equal, but are positive.", "section_idx": 3, "section_name": "Spacing and non-spacing characters", "target_page_ids": [ 1209, 31247, 44365, 620604, 160987, 1172087, 64105, 7951270 ], "anchor_spans": [ [ 121, 125 ], [ 161, 169 ], [ 175, 185 ], [ 269, 278 ], [ 413, 447 ], [ 462, 470 ], [ 477, 494 ], [ 546, 554 ] ] }, { "plaintext": "There exist also non-spacing graphic characters. Most of non-spacing characters are modifiers, also called combining characters in Unicode, such as diacritical marks. Although non-spacing graphic characters are uncommon in traditional code pages, there are many such in Unicode. A combining character has its distinct glyph, but it applies to a character box of another character, a spacing one. In some historical systems such as line printers this was implemented as overstrike.", "section_idx": 3, "section_name": "Spacing and non-spacing characters", "target_page_ids": [ 497884, 497884, 8439, 194376, 45879, 779807 ], "anchor_spans": [ [ 57, 78 ], [ 107, 126 ], [ 148, 157 ], [ 235, 244 ], [ 431, 443 ], [ 469, 479 ] ] }, { "plaintext": "Note that not all modifiers are non-spacing– there exists Spacing Modifier Letters Unicode block.", "section_idx": 3, "section_name": "Spacing and non-spacing characters", "target_page_ids": [ 5921334 ], "anchor_spans": [ [ 58, 82 ] ] }, { "plaintext": " encoded character", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 5295 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " ASCII", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 586 ], "anchor_spans": [ [ 1, 6 ] ] } ]

[ "Character_encoding" ]

[]

[ { "plaintext": "In electrical engineering, ground or earth is a reference point in an electrical circuit from which voltages are measured, a common return path for electric current, or a direct physical connection to the Earth.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 9531, 9559, 32549, 6207 ], "anchor_spans": [ [ 3, 25 ], [ 70, 88 ], [ 100, 107 ], [ 148, 164 ] ] }, { "plaintext": "Electrical circuits may be connected to ground for several reasons. Exposed conductive parts of electrical equipment are connected to ground, to protect users from electrical shock hazard. If internal insulation fails, dangerous voltages may appear on the exposed conductive parts. Connecting exposed parts to ground will allow circuit breakers (or RCDs) to interrupt power supply in the event of a fault. In electric power distribution systems, a protective earth (PE) conductor is an essential part of the safety provided by the earthing system.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 211889, 235899, 530715, 2251965 ], "anchor_spans": [ [ 175, 187 ], [ 328, 343 ], [ 349, 352 ], [ 531, 546 ] ] }, { "plaintext": "Connection to ground also limits the build-up of static electricity when handling flammable products or electrostatic-sensitive devices. In some telegraph and power transmission circuits, the ground itself can be used as one conductor of the circuit, saving the cost of installing a separate return conductor (see single-wire earth return and earth-return telegraph).", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 200136, 5903372, 30010, 38822, 198984, 369526, 63657523 ], "anchor_spans": [ [ 49, 67 ], [ 104, 134 ], [ 145, 154 ], [ 159, 177 ], [ 225, 234 ], [ 314, 338 ], [ 343, 365 ] ] }, { "plaintext": "For measurement purposes, the Earth serves as a (reasonably) constant potential reference against which other potentials can be measured. An electrical ground system should have an appropriate current-carrying capability to serve as an adequate zero-voltage reference level. In electronic circuit theory, a \"ground\" is usually idealized as an infinite source or sink for charge, which can absorb an unlimited amount of current without changing its potential. Where a real ground connection has a significant resistance, the approximation of zero potential is no longer valid. Stray voltages or earth potential rise effects will occur, which may create noise in signals or produce an electric shock hazard if large enough.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 8707643, 2235900, 11513302, 8929041 ], "anchor_spans": [ [ 278, 296 ], [ 352, 366 ], [ 576, 589 ], [ 594, 614 ] ] }, { "plaintext": "The use of the term ground (or earth) is so common in electrical and electronics applications that circuits in portable electronic devices, such as cell phones and media players, as well as circuits in vehicles, may be spoken of as having a \"ground\" or chassis ground connection without any actual connection to the Earth, despite \"common\" being a more appropriate term for such a connection. That is usually a large conductor attached to one side of the power supply (such as the \"ground plane\" on a printed circuit board), which serves as the common return path for current from many different components in the circuit.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 657187, 19644137, 1560437, 32410, 3435954, 219042, 41218, 65910 ], "anchor_spans": [ [ 111, 138 ], [ 148, 158 ], [ 164, 176 ], [ 202, 210 ], [ 253, 267 ], [ 455, 467 ], [ 482, 494 ], [ 501, 522 ] ] }, { "plaintext": "Long-distance electromagnetic telegraph systems from 1820 onwards used two or more wires to carry the signal and return currents. It was discovered by German scientist Carl August Steinheil in 1836–1837, that the ground could be used as the return path to complete the circuit, making the return wire unnecessary. Steinheil was not the first to do this, but he was not aware of earlier experimental work, and he was the first to do it on an in-service telegraph, thus making the principle known to telegraph engineers generally. However, there were problems with this system, exemplified by the transcontinental telegraph line constructed in 1861 by the Western Union Company between St. Joseph, Missouri, and Sacramento, California. During dry weather, the ground connection often developed a high resistance, requiring water to be poured on the ground rod to enable the telegraph to work or phones to ring.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 9450, 5100939, 149369, 29631, 2841659 ], "anchor_spans": [ [ 30, 39 ], [ 168, 189 ], [ 685, 705 ], [ 711, 733 ], [ 848, 858 ] ] }, { "plaintext": "In the late nineteenth century, when telephony began to replace telegraphy, it was found that the currents in the earth induced by power systems, electric railways, other telephone and telegraph circuits, and natural sources including lightning caused unacceptable interference to the audio signals, and the two-wire or 'metallic circuit' system was reintroduced around 1883.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Electrical power distribution systems are often connected to earth ground to limit the voltage that can appear on distribution circuits. A distribution system insulated from earth ground may attain a high potential due to transient voltages caused by static electricity or accidental contact with higher potential circuits. An earth ground connection of the system dissipates such potentials and limits the rise in voltage of the grounded system.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In a mains electricity (AC power) wiring installation, the term ground conductor typically refers to two different conductors or conductor systems as listed below:", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [ 175959, 1065627 ], "anchor_spans": [ [ 5, 22 ], [ 64, 70 ] ] }, { "plaintext": "Equipment bonding conductors or equipment ground conductors (EGC) provide a low impedance path between normally non-current-carrying metallic parts of equipment and one of the conductors of that electrical system's source. If any exposed metal part should become energized (fault), such as by a frayed or damaged insulator, it creates a short circuit, causing the overcurrent device (circuit breaker or fuse) to open, clearing (disconnecting) the fault. It is important to note this action occurs regardless of whether there is a connection to the physical ground (earth); the earth itself has no role in this fault-clearing process since current must return to its source; however, the sources are very frequently connected to the physical ground (earth). (see Kirchhoff's circuit laws). By bonding (interconnecting) all exposed non-current carrying metal objects together, as well as to other metallic objects such as pipes or structural steel, they should remain near the same voltage potential, thus reducing the chance of a shock. This is especially important in bathrooms where one may be in contact with several different metallic systems such as supply and drain pipes and appliance frames. When a conductive system is to be electrically connected to the physical ground (earth), one puts the equipment bonding conductor and the grounding electrode conductor at the same potential (for example, see Bonding Conductor below).", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [ 591253 ], "anchor_spans": [ [ 762, 786 ] ] }, { "plaintext": "A (GEC) is used to connect the system grounded (\"neutral\") conductor, or the equipment to a grounding electrode, or a point on the grounding electrode system. This is called \"system grounding\" and most electrical systems are required to be grounded. The U.S. NEC and the UK's BS 7671 list systems that are required to be grounded. According to the NEC, the purpose of connecting an electrical system to the physical ground (earth) is to limit the voltage imposed by lightning events and contact with higher voltage lines. In the past, water supply pipes were used as grounding electrodes, but due to the increased use of plastic pipes, which are poor conductors, the use of a specific grounding electrode is often mandated by regulating authorities. The same type of ground applies to radio antennas and to lightning protection systems.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [ 2118467, 684928 ], "anchor_spans": [ [ 277, 284 ], [ 536, 548 ] ] }, { "plaintext": "Permanently installed electrical equipment, unless not required to, has permanently connected grounding conductors. Portable electrical devices with metal cases may have them connected to earth ground by a pin on the attachment plug (see Domestic AC power plugs and sockets). The size of power grounding conductors is usually regulated by local or national wiring regulations.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [ 773271 ], "anchor_spans": [ [ 238, 273 ] ] }, { "plaintext": "Strictly speaking, the terms grounding or earthing are meant to refer to an electrical connection to ground/earth. Bonding is the practice of intentionally electrically connecting metallic items not designed to carry electricity. This brings all the bonded items to the same electrical potential as a protection from electrical shock. The bonded items can then be connected to ground to eliminate foreign voltages.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [ 3581021 ], "anchor_spans": [ [ 115, 122 ] ] }, { "plaintext": "In electricity supply systems, an earthing (grounding) system defines the electrical potential of the conductors relative to that of the Earth's conductive surface. The choice of earthing system has implications for the safety and electromagnetic compatibility of the power supply. Regulations for earthing systems vary considerably between different countries.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A functional earth connection serves more than protecting against electrical shock, as such a connection may carry current during the normal operation of a device. Such devices include surge suppression, electromagnetic-compatibility filters, some types of antennas, and various measurement instruments. Generally the protective earth system is also used as a functional earth, though this requires care.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Distribution power systems may be solidly grounded, with one circuit conductor directly connected to an earth grounding electrode system. Alternatively, some amount of electrical impedance may be connected between the distribution system and ground, to limit the current that can flow to earth. The impedance may be a resistor, or an inductor (coil). In a high-impedance grounded system, the fault current is limited to a few amperes (exact values depend on the voltage class of the system); a low-impedance grounded system will permit several hundred amperes to flow on a fault. A large solidly grounded distribution system may have thousands of amperes of ground fault current.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [ 41957 ], "anchor_spans": [ [ 168, 188 ] ] }, { "plaintext": "In a polyphase AC system, an artificial neutral grounding system may be used. Although no phase conductor is directly connected to ground, a specially constructed transformer (a \"zig zag\" transformer) blocks the power frequency current from flowing to earth, but allows any leakage or transient current to flow to ground.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [ 1241344 ], "anchor_spans": [ [ 178, 199 ] ] }, { "plaintext": "Low-resistance grounding systems use a neutral grounding resistor (NGR) to limit the fault current to 25A or greater. Low resistance grounding systems will have a time rating (say, 10 seconds) that indicates how long the resistor can carry the fault current before overheating. A ground fault protection relay must trip the breaker to protect the circuit before overheating of the resistor occurs.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "High-resistance grounding (HRG) systems use an NGR to limit the fault current to 25A or less. They have a continuous rating, and are designed to operate with a single-ground fault. This means that the system will not immediately trip on the first ground fault. If a second ground fault occurs, a ground fault protection relay must trip the breaker to protect the circuit. On an HRG system, a sensing resistor is used to continuously monitor system continuity. If an open-circuit is detected (e.g., due to a broken weld on the NGR), the monitoring device will sense voltage through the sensing resistor and trip the breaker. Without a sensing resistor, the system could continue to operate without ground protection (since an open circuit condition would mask the ground fault) and transient overvoltages could occur.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Where the danger of electric shock is high, special ungrounded power systems may be used to minimize possible leakage current to ground. Examples of such installations include patient care areas in hospitals, where medical equipment is directly connected to a patient and must not permit any power-line current to pass into the patient's body. Medical systems include monitoring devices to warn of any increase of leakage current. On wet construction sites or in shipyards, isolation transformers may be provided so that a fault in a power tool or its cable does not expose users to shock hazard.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Circuits used to feed sensitive audio/video production equipment or measurement instruments may be fed from an isolated ungrounded technical power system to limit the injection of noise from the power system.", "section_idx": 2, "section_name": "Building wiring installations", "target_page_ids": [ 1047958 ], "anchor_spans": [ [ 131, 146 ] ] }, { "plaintext": "In single-wire earth return (SWER) AC electrical distribution systems, costs are saved by using just a single high voltage conductor for the power grid, while routing the AC return current through the earth. This system is mostly used in rural areas where large earth currents will not otherwise cause hazards.", "section_idx": 3, "section_name": "Power transmission", "target_page_ids": [ 369526, 20344155 ], "anchor_spans": [ [ 3, 27 ], [ 141, 151 ] ] }, { "plaintext": "Some high-voltage direct-current (HVDC) power transmission systems use the ground as second conductor. This is especially common in schemes with submarine cables, as sea water is a good conductor. Buried grounding electrodes are used to make the connection to the earth. The site of these electrodes must be chosen carefully to prevent electrochemical corrosion on underground structures.", "section_idx": 3, "section_name": "Power transmission", "target_page_ids": [ 47716 ], "anchor_spans": [ [ 5, 32 ] ] }, { "plaintext": "A particular concern in design of electrical substations is earth potential rise. When very large fault currents are injected into the earth, the area around the point of injection may rise to a high potential with respect to points distant from it. This is due to the limited finite conductivity of the layers of soil in the earth of the substation. The gradient of the voltage (the change in voltage across the distance to the injection point) may be so high that two points on the ground may be at significantly different potentials. This gradient creates a hazard to anyone standing on the earth in an area of the electrical substation that is insufficiently insulated from ground. Pipes, rails, or communication wires entering a substation may see different ground potentials inside and outside the substation, creating a dangerous touch voltage for unsuspecting persons who might touch those pipes, rails, or wires. This problem is alleviated by creating a low-impedance equipotential bonding plane installed in accordance with IEEE 80, within the substation. This plane eliminates voltage gradients and ensures that any fault is cleared within three voltage cycles.", "section_idx": 3, "section_name": "Power transmission", "target_page_ids": [ 320217, 8929041, 8929041 ], "anchor_spans": [ [ 34, 55 ], [ 60, 80 ], [ 837, 850 ] ] }, { "plaintext": "|- align = \"center\"", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| ", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|width = \"25\"| ", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| ", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|width = \"25\"| ", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| ", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|- align = \"center\"", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| Signal ground", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| ", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| Chassis ground", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| Earth ground", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Signal grounds serve as return paths for signals and power (at extra-low voltages, less than about 50 V) within equipment, and on the signal interconnections between equipment. Many electronic designs feature a single return that acts as a reference for all signals. Power and signal grounds often get connected, usually through the metal case of the equipment. Designers of printed circuit boards must take care in the layout of electronic systems so that high-power or rapidly switching currents in one part of a system do not inject noise into low-level sensitive parts of a system due to some common impedance in the grounding traces of the layout.", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [ 2446565, 65910 ], "anchor_spans": [ [ 63, 80 ], [ 375, 396 ] ] }, { "plaintext": "Voltage is defined as the difference of electric potentials between points in an electric field. A voltmeter is used to measure the potential difference between some point and a reference point. This common reference point is denoted \"ground\" and considered to have zero potential. Signals are defined with respect to signal ground, which may be connected to a power ground. A system where the system ground is not connected to another circuit or to earth (in which there may still be AC coupling between those circuits) is often referred to as a floating ground or double-insulated.", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [ 32549, 59615, 32743, 275871, 2293660, 1065627, 40843, 17388115, 856432 ], "anchor_spans": [ [ 0, 7 ], [ 40, 58 ], [ 99, 108 ], [ 282, 288 ], [ 318, 331 ], [ 361, 373 ], [ 485, 496 ], [ 547, 562 ], [ 566, 582 ] ] }, { "plaintext": "Some devices require a connection to the mass of earth to function correctly, as distinct from any purely protective role. Such a connection is known as a functional earth- for example some long wavelength antenna structures require a functional earth connection, which generally should not be indiscriminately connected to the supply protective earth, as the introduction of transmitted radio frequencies into the electrical distribution network is both illegal and potentially dangerous. Because of this separation, a purely functional ground should not normally be relied upon to perform a protective function.", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "To avoid accidents, such functional grounds are normally wired in white or cream cable, and not green or green/yellow.", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In television stations, recording studios, and other installations where signal quality is critical, a special signal ground known as a \"technical ground\" (or \"technical earth\", \"special earth\", and \"audio earth\") is often installed, to prevent ground loops. This is basically the same thing as an AC power ground, but no general appliance ground wires are allowed any connection to it, as they may carry electrical interference. For example, only audio equipment is connected to the technical ground in a recording studio. In most cases, the studio's metal equipment racks are all joined together with heavy copper cables (or flattened copper tubing or busbars) and similar connections are made to the technical ground. Great care is taken that no general chassis grounded appliances are placed on the racks, as a single AC ground connection to the technical ground will destroy its effectiveness. For particularly demanding applications, the main technical ground may consist of a heavy copper pipe, if necessary fitted by drilling through several concrete floors, such that all technical grounds may be connected by the shortest possible path to a grounding rod in the basement.", "section_idx": 4, "section_name": "Electronics", "target_page_ids": [ 29831, 234751, 940296, 1029195 ], "anchor_spans": [ [ 3, 13 ], [ 24, 41 ], [ 245, 256 ], [ 654, 660 ] ] }, { "plaintext": "Certain types of radio antennas (or their feedlines) require a connection to ground. Since the radio frequencies of the current in radio antennas are far higher than the 50/60Hz frequency of the power line, radio grounding systems use different principles from AC power grounding. The \"third wire\" safety grounds in AC utility building wiring were not designed for and cannot be used for this purpose. The long utility ground wires have high impedance at certain frequencies. In the case of a transmitter, the RF current flowing through the ground wires can radiate radio frequency interference and induce hazardous voltages on grounded metal parts of other appliances, so separate ground systems are used.", "section_idx": 5, "section_name": "Radio antennas", "target_page_ids": [ 187317, 1826418, 42852, 41957, 1072324 ], "anchor_spans": [ [ 17, 31 ], [ 42, 50 ], [ 96, 113 ], [ 445, 454 ], [ 570, 598 ] ] }, { "plaintext": "Monopole antennas operating at lower frequencies, below 20MHz, use the Earth as part of the antenna, as a conductive plane to reflect the radio waves. These include the T and inverted L antenna, umbrella antenna and the mast radiator used by AM radio stations. The feedline from the transmitter is connected between the antenna and ground, so it requires a grounding (Earthing) system under the antenna to make contact with the soil to collect the return current. In lower power transmitters and radio receivers, the ground connection can be as simple as one or more metal rods or stakes driven into the earth, or an electrical connection to a building's metal water piping which extends into the earth. However, in transmitting antennas the ground system carries the full output current of the transmitter, so the resistance of an inadequate ground contact can be a major loss of transmitter power. The ground system functions as a capacitor plate, to receive the displacement current from the antenna and return it to the ground side of the transmitter's feedline, so it is preferably located directly under the antenna.", "section_idx": 5, "section_name": "Radio antennas", "target_page_ids": [ 2874126, 2046972, 7996832, 2044847, 491851, 4932111, 555119 ], "anchor_spans": [ [ 0, 16 ], [ 170, 194 ], [ 196, 212 ], [ 221, 234 ], [ 500, 514 ], [ 940, 949 ], [ 972, 992 ] ] }, { "plaintext": "Medium to high power transmitters usually have an extensive ground system consisting of bare copper cables buried in the earth under the antenna, to lower resistance. Since for the omnidirectional antennas used on these bands the Earth currents travel radially toward the ground point from all directions, the grounding system usually consists of a radial pattern of buried cables extending outward under the antenna in all directions, connected together to the ground side of the transmitter's feedline at a terminal next to the base of the antenna.", "section_idx": 5, "section_name": "Radio antennas", "target_page_ids": [ 342372, 1826418 ], "anchor_spans": [ [ 182, 205 ], [ 496, 504 ] ] }, { "plaintext": "The transmitter power lost in the ground resistance, and so the efficiency of the antenna, depends on the soil conductivity. This varies widely; marshy ground or ponds, particularly salt water, provide the lowest resistance ground, while dry rocky or sandy soil are the highest. The power loss per square meter in the ground is proportional to the square of the transmitter current density flowing in the earth. The current density, and power dissipated, increases the closer one gets to the ground terminal at the base of the antenna, so the radial ground system can be thought of as providing a higher conductivity medium, copper, for the ground current to flow through, in the parts of the ground carrying high current density, to reduce power losses.", "section_idx": 5, "section_name": "Radio antennas", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A standard ground system widely used for mast radiator broadcasting antennas operating in the MF and LF bands consists of 120 equally-spaced buried radial ground wires extending out one quarter of a wavelength (.25, 90 electrical degrees) from the antenna. No. 8 to 10 gauge soft-drawn copper wire is typically used, buried 4 to 10 inches deep. For AM broadcast band antennas this requires a circular land area extending from the mast . This is usually planted with grass, which is kept mowed short as tall grass can increase power loss in certain circumstances. If the land area available is too limited for such long radials, they can in many cases be replaced by a greater number of shorter radials, or a smaller number of longer radials.", "section_idx": 5, "section_name": "Radio antennas", "target_page_ids": [ 2044847, 160519, 160518, 33125, 113509 ], "anchor_spans": [ [ 41, 54 ], [ 94, 96 ], [ 101, 103 ], [ 199, 209 ], [ 351, 368 ] ] }, { "plaintext": "In transmitting antennas a second cause of power wastage is dielectric power losses of the electric field (displacement current) of the antenna passing through the earth to reach the ground wires. For antennas near a half-wavelength high (180 electrical degrees) the antenna has a voltage maximum (antinode) near its base, which results in strong electric fields in the earth above the ground wires near the mast where the displacement current enters the ground. To reduce this loss these antennas often use a conductive copper ground screen under the antenna connected to the buried ground wires, either lying on the ground or elevated a few feet, to shield the ground from the electric field.", "section_idx": 5, "section_name": "Radio antennas", "target_page_ids": [ 7090506, 41092, 555119, 998070, 555119 ], "anchor_spans": [ [ 60, 83 ], [ 91, 105 ], [ 107, 127 ], [ 300, 308 ], [ 425, 445 ] ] }, { "plaintext": "In a few cases where rocky or sandy soil has too high a resistance for a buried ground, a counterpoise is used. This is a radial network of wires similar to that in a buried ground system, but lying on the surface or suspended a few feet above the ground. It acts as a capacitor plate, capacitively coupling the feedline to conductive layers of the earth.", "section_idx": 5, "section_name": "Radio antennas", "target_page_ids": [ 28945794, 4932111 ], "anchor_spans": [ [ 90, 102 ], [ 271, 280 ] ] }, { "plaintext": "At lower frequencies the resistance of the ground system is a more critical factor because of the small radiation resistance of the antenna. In the LF and VLF bands, construction height limitations require that electrically short antennas be used, shorter than the fundamental resonant length of one quarter of a wavelength (). A quarter wave monopole has a radiation resistance of around 25 to 36 ohms, but below the resistance decreases with the square of the ratio of height to wavelength. The power fed to an antenna is split between the radiation resistance, which represents power emitted as radio waves, the desired function of the antenna, and the ohmic resistance of the ground system, which results in power wasted as heat. As the wavelength gets longer in relation to antenna height, the radiation resistance of the antenna decreases so the ground resistance constitutes a larger proportion of the input resistance of the antenna and consumes more of the transmitter power. Antennas in the VLF band often have a resistance of less than one ohm, and even with extremely low resistance ground systems 50% to 90% of the transmitter power may be wasted in the ground system.", "section_idx": 5, "section_name": "Radio antennas", "target_page_ids": [ 160518, 160505, 41091, 41660, 33125, 342381, 4462484, 4462484 ], "anchor_spans": [ [ 149, 151 ], [ 156, 159 ], [ 212, 230 ], [ 278, 286 ], [ 314, 324 ], [ 360, 380 ], [ 400, 403 ], [ 1058, 1061 ] ] }, { "plaintext": "Lightning protection systems are designed to mitigate the effects of lightning through connection to extensive grounding systems that provide a large surface area connection to earth. The large area is required to dissipate the high current of a lightning strike without damaging the system conductors by excess heat. Since lightning strikes are pulses of energy with very high frequency components, grounding systems for lightning protection tend to use short straight runs of conductors to reduce the self-inductance and skin effect.", "section_idx": 6, "section_name": "Lightning protection systems", "target_page_ids": [ 165146, 261642 ], "anchor_spans": [ [ 508, 518 ], [ 523, 534 ] ] }, { "plaintext": "In an electrical substation a ground (earth) mat is a mesh of conductive material installed at places where a person would stand to operate a switch or other apparatus; it is bonded to the local supporting metal structure and to the handle of the switchgear, so that the operator will not be exposed to a high differential voltage due to a fault in the substation.", "section_idx": 7, "section_name": "Ground (earth) mat", "target_page_ids": [ 320217 ], "anchor_spans": [ [ 6, 27 ] ] }, { "plaintext": "In the vicinity of electrostatic sensitive devices, a ground (earth) mat or grounding (earthing) mat is used to ground static electricity generated by people and moving equipment. There are two types used in static control: Static Dissipative Mats, and Conductive Mats.", "section_idx": 7, "section_name": "Ground (earth) mat", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A static dissipative mat that rests on a conductive surface (commonly the case in military facilities) are typically made of 3 layers (3-ply) with static dissipative vinyl layers surrounding a conductive substrate which is electrically attached to ground (earth). For commercial uses, static dissipative rubber mats are traditionally used that are made of 2 layers (2-ply) with a tough solder resistant top static dissipative layer that makes them last longer than the vinyl mats, and a conductive rubber bottom. Conductive mats are made of carbon and used only on floors for the purpose of drawing static electricity to ground as quickly as possible. Normally conductive mats are made with cushioning for standing and are referred to as \"anti-fatigue\" mats.", "section_idx": 7, "section_name": "Ground (earth) mat", "target_page_ids": [ 47889743 ], "anchor_spans": [ [ 487, 504 ] ] }, { "plaintext": "For a static dissipative mat to be reliably grounded it must be attached to a path to ground. Normally, both the mat and the wrist strap are connected to ground by using a common point ground system (CPGS).", "section_idx": 7, "section_name": "Ground (earth) mat", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In computer repair shops and electronics manufacturing workers must be grounded before working on devices sensitive to voltages capable of being generated by humans. For that reason static dissipative mats can be and are also used on production assembly floors as \"floor runner\" along the assembly line to draw static generated by people walking up and down.", "section_idx": 7, "section_name": "Ground (earth) mat", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Isolation is a mechanism that defeats grounding. It is frequently used with low-power consumer devices, and when engineers, hobbyists, or repairmen are working on circuits that would normally be operated using the power line voltage. Isolation can be accomplished by simply placing a \"1:1 wire ratio\" transformer with an equal number of turns between the device and the regular power service, but applies to any type of transformer using two or more coils electrically insulated from each other.", "section_idx": 8, "section_name": "Isolation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For an isolated device, touching a single powered conductor does not cause a severe shock, because there is no path back to the other conductor through the ground. However, shocks and electrocution may still occur if both poles of the transformer are contacted by bare skin. Previously it was suggested that repairmen \"work with one hand behind their back\" to avoid touching two parts of the device under test at the same time, thereby preventing a current from crossing through the chest and interrupting cardiac rhythms or causing cardiac arrest.", "section_idx": 8, "section_name": "Isolation", "target_page_ids": [ 60575 ], "anchor_spans": [ [ 533, 547 ] ] }, { "plaintext": "Generally every AC power line transformer acts as an isolation transformer, and every step up or down has the potential to form an isolated circuit. However, this isolation would prevent failed devices from blowing fuses when shorted to their ground conductor. The isolation that could be created by each transformer is defeated by always having one leg of the transformers grounded, on both sides of the input and output transformer coils. Power lines also typically ground one specific wire at every pole, to ensure current equalization from pole to pole if a short to ground is occurring.", "section_idx": 8, "section_name": "Isolation", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In the past, grounded appliances have been designed with internal isolation to a degree that allowed the simple disconnection of ground by cheater plugs without apparent problem (a dangerous practice, since the safety of the resulting floating equipment relies on the insulation in its power transformer). Modern appliances however often include power entry modules which are designed with deliberate capacitive coupling between the AC power lines and chassis, to suppress electromagnetic interference. This results in a significant leakage current from the power lines to ground. If the ground is disconnected by a cheater plug or by accident, the resulting leakage current can cause mild shocks, even without any fault in the equipment. Even small leakage currents are a significant concern in medical settings, as the accidental disconnection of ground can introduce these currents into sensitive parts of the human body. As a result, medical power supplies are designed to have low capacitance.", "section_idx": 8, "section_name": "Isolation", "target_page_ids": [ 26230192, 8857882 ], "anchor_spans": [ [ 139, 151 ], [ 346, 364 ] ] }, { "plaintext": "Class II appliances and power supplies (such as cell phone chargers) do not provide any ground connection, and are designed to isolate the output from input. Safety is ensured by double-insulation, so that two failures of insulation are required to cause a shock.", "section_idx": 8, "section_name": "Isolation", "target_page_ids": [ 856432 ], "anchor_spans": [ [ 0, 8 ] ] }, { "plaintext": " Appliance classes", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 856432 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Ground constants", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 41216 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Ring ground", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 31948597 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Ground loop (electricity)", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 940296 ], "anchor_spans": [ [ 1, 26 ] ] }, { "plaintext": " Ground wire (transmission line)", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 1355057 ], "anchor_spans": [ [ 1, 32 ] ] }, { "plaintext": " Isolated ground", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 31296909 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Phantom circuit", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 41507 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Floating ground", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 17388115 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Soil resistivity", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 33533975 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Ufer ground", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 12237604 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Virtual ground", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 564641 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Federal Standard 1037C in support of MIL-STD-188", "section_idx": 11, "section_name": "References", "target_page_ids": [ 37310, 41882 ], "anchor_spans": [ [ 1, 23 ], [ 38, 49 ] ] }, { "plaintext": " Circuit Grounds and Grounding Practices", "section_idx": 12, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Electrical Safety chapter from Lessons In Electric Circuits Vol 1 DC book and series.", "section_idx": 12, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Grounding for Low- and High- Frequency Circuits (PDF)— Analog Devices Application Note", "section_idx": 12, "section_name": "External links", "target_page_ids": [ 24077, 644341 ], "anchor_spans": [ [ 50, 53 ], [ 56, 70 ] ] }, { "plaintext": " An IC Amplifier User’s Guide to Decoupling, Grounding, and Making Things Go Right for a Change (PDF)— Analog Devices Application Note", "section_idx": 12, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " The Electromagnetic Telegraph, by J. B. Calvert", "section_idx": 12, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Electric_power", "Electrical_safety", "Electrical_wiring", "Power_engineering", "Electric_power_distribution" ]

[ "ground (electricity)", "earth", "electrical ground", "electrical earth", "0 V", "0V", "+0 V", "+0V", "circuit ground", "voltage reference", "GND" ]

[ { "plaintext": "In telecommunication, ground constants are the electrical parameters of earth: electrical conductivity, σ, electrical permittivity, ε, and magnetic permeability, μ.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 37738, 61580, 53933, 754487 ], "anchor_spans": [ [ 3, 20 ], [ 72, 77 ], [ 79, 102 ], [ 107, 130 ], [ 139, 160 ] ] }, { "plaintext": "The values of these parameters vary with the local chemical composition and density of the Earth. For a propagating electromagnetic wave, such as a surface wave propagating along the surface of the Earth, these parameters vary with frequency and direction. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 9426, 41763, 10779 ], "anchor_spans": [ [ 116, 136 ], [ 148, 160 ], [ 232, 241 ] ] }, { "plaintext": "Ground", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 41215 ], "anchor_spans": [ [ 0, 6 ] ] } ]

[ "Telecommunications_engineering" ]

[]

[ { "plaintext": "Ground loop may refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Ground loop (electricity), an unwanted electric current that flows in a conductor connecting two points inadvertently having different potentials", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 940296 ], "anchor_spans": [ [ 1, 26 ] ] }, { "plaintext": " Ground loop (aviation), the rapid circular rotation of an aircraft in the horizontal plane while on the ground", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 940299 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Ground-coupled heat exchanger, an underground heat exchanger loop that can capture or dissipate heat to or from the ground", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 4813788 ], "anchor_spans": [ [ 1, 30 ] ] } ]

[]

[]

[ { "plaintext": "In electrical engineering, a ground plane is an electrically conductive surface, usually connected to electrical ground.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 9531, 198984, 41215 ], "anchor_spans": [ [ 3, 25 ], [ 61, 71 ], [ 113, 119 ] ] }, { "plaintext": "The term has two different meanings in separate areas of electrical engineering.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In antenna theory, a ground plane is a conducting surface large in comparison to the wavelength, such as the Earth, which is connected to the transmitter's ground wire and serves as a reflecting surface for radio waves.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 187317, 33125, 61164, 98132 ], "anchor_spans": [ [ 3, 10 ], [ 85, 95 ], [ 142, 153 ], [ 207, 217 ] ] }, { "plaintext": "In printed circuit boards, a ground plane is a large area of copper foil on the board which is connected to the power supply ground terminal and serves as a return path for current from different components on the board.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 65910, 41215 ], "anchor_spans": [ [ 3, 24 ], [ 125, 131 ] ] }, { "plaintext": "In telecommunication, a ground plane is a flat or nearly flat horizontal conducting surface that serves as part of an antenna, to reflect the radio waves from the other antenna elements. The plane does not necessarily have to be connected to ground to be used as a reflecting surface for radio waves. Ground plane shape and size play major roles in determining its radiation characteristics including gain.", "section_idx": 1, "section_name": "Radio antenna theory", "target_page_ids": [ 33094374, 187317, 98132, 41215, 49693 ], "anchor_spans": [ [ 3, 20 ], [ 118, 125 ], [ 142, 152 ], [ 243, 249 ], [ 402, 406 ] ] }, { "plaintext": "To function as a ground plane, the conducting surface must be at least a quarter of the wavelength (λ/4) of the radio waves in radius. In lower frequency antennas, such as the mast radiators used for broadcast antennas, the Earth itself (or a body of water such as a salt marsh or ocean) is used as a ground plane. For higher frequency antennas, in the VHF or UHF range, the ground plane can be smaller, and metal disks, screens and wires are used as ground planes. At upper VHF and UHF, the metal skin of a car or aircraft can serve as a ground plane for whip antennas projecting from it. In microstrip antennas and printed monopole antennas an area of copper foil on the opposite side of a printed circuit board serves as a ground plane. The ground plane need not be a continuous surface. In the ground plane antenna style whip antenna, the \"plane\" consists of several wires λ/4 long radiating from the base of a quarter-wave whip antenna.", "section_idx": 1, "section_name": "Radio antenna theory", "target_page_ids": [ 33125, 10779, 2044847, 69480, 160501, 465189, 2021939, 2874126, 65910, 465189 ], "anchor_spans": [ [ 88, 98 ], [ 148, 157 ], [ 180, 193 ], [ 358, 361 ], [ 365, 368 ], [ 565, 577 ], [ 603, 621 ], [ 635, 651 ], [ 702, 723 ], [ 839, 851 ] ] }, { "plaintext": "The radio waves from an antenna element that reflect off a ground plane appear to come from a mirror image of the antenna located on the other side of the ground plane. In a monopole antenna, the radiation pattern of the monopole plus the virtual \"image antenna\" make it appear as a two element center-fed dipole antenna. So a monopole mounted over an ideal ground plane has a radiation pattern identical to a dipole antenna. The feedline from the transmitter or receiver is connected between the bottom end of the monopole element and the ground plane. The ground plane must have good conductivity; any resistance in the ground plane is in series with the antenna, and serves to dissipate power from the transmitter.", "section_idx": 1, "section_name": "Radio antenna theory", "target_page_ids": [ 41251, 465156 ], "anchor_spans": [ [ 249, 262 ], [ 307, 321 ] ] }, { "plaintext": "A ground plane on a printed circuit board (PCB) is a large area or layer of copper foil connected to the circuit's ground point, usually one terminal of the power supply. It serves as the return path for current from many different components.", "section_idx": 2, "section_name": "Printed circuit boards", "target_page_ids": [ 65910, 41215, 219042, 6207 ], "anchor_spans": [ [ 20, 41 ], [ 115, 121 ], [ 157, 169 ], [ 205, 212 ] ] }, { "plaintext": "A ground plane is often made as large as possible, covering most of the area of the PCB which is not occupied by circuit traces. In multilayer PCBs, it is often a separate layer covering the entire board. This serves to make circuit layout easier, allowing the designer to ground any component without having to run additional traces; component leads needing grounding are routed directly through a hole in the board to the ground plane on another layer. The large area of copper also conducts the large return currents from many components without significant voltage drops, ensuring that the ground connection of all the components are at the same reference potential.", "section_idx": 2, "section_name": "Printed circuit boards", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In digital and radio frequency PCBs, the major reason for using large ground planes is to reduce electrical noise and interference through ground loops and to prevent crosstalk between adjacent circuit traces. When digital circuits switch state, large current pulses flow from the active devices (transistors or integrated circuits) through the ground circuit. If the power supply and ground traces have significant impedance, the voltage drop across them may create noise voltage pulses that disturb other parts of the circuit (ground bounce). The large conducting area of the ground plane has much lower impedance than a circuit trace, so the current pulses cause less disturbance.", "section_idx": 2, "section_name": "Printed circuit boards", "target_page_ids": [ 42852, 3966982, 940296, 2995499 ], "anchor_spans": [ [ 15, 30 ], [ 97, 113 ], [ 139, 150 ], [ 167, 176 ] ] }, { "plaintext": "In addition, a ground plane under printed circuit traces can reduce crosstalk between adjacent traces. When two traces run parallel, an electrical signal in one can be coupled into the other through electromagnetic induction by magnetic field lines from one linking the other; this is called crosstalk. When a ground plane layer is present underneath, it forms a transmission line with the trace. The oppositely-directed return currents flow through the ground plane directly beneath the trace. This confines most of the electromagnetic fields to the area near the trace and consequently reduces crosstalk.", "section_idx": 2, "section_name": "Printed circuit boards", "target_page_ids": [ 65888, 2995499, 41811 ], "anchor_spans": [ [ 200, 225 ], [ 293, 302 ], [ 365, 382 ] ] }, { "plaintext": "A power plane is often used in addition to a ground plane in a multilayer circuit board, to distribute DC power to the active devices. The two facing areas of copper create a large parallel plate decoupling capacitor that prevents noise from being coupled from one circuit to another through the power supply.", "section_idx": 2, "section_name": "Printed circuit boards", "target_page_ids": [ 4397993, 219042 ], "anchor_spans": [ [ 198, 218 ], [ 299, 311 ] ] }, { "plaintext": "Ground planes are sometimes split and then connected by a thin trace. This allows the separation of analog and digital sections of a board or the inputs and outputs of amplifiers. The thin trace has low enough impedance to keep the two sides very close to the same potential while keeping the ground currents of one side from coupling into the other side, causing ground loop.", "section_idx": 2, "section_name": "Printed circuit boards", "target_page_ids": [ 41957, 940296 ], "anchor_spans": [ [ 212, 221 ], [ 366, 377 ] ] }, { "plaintext": " List of electronics topics", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 295156 ], "anchor_spans": [ [ 1, 27 ] ] }, { "plaintext": " Power plane ", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 65910 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Microstrip and Stripline", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 2022356, 4269572 ], "anchor_spans": [ [ 1, 11 ], [ 16, 25 ] ] }, { "plaintext": " Line-of-sight propagation ", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 60455 ], "anchor_spans": [ [ 1, 26 ] ] }, { "plaintext": " Radio electronics and Radio propagation ", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 13485805, 271195 ], "anchor_spans": [ [ 1, 18 ], [ 23, 40 ] ] }, { "plaintext": " Printed circuit board milling", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 1029949 ], "anchor_spans": [ [ 1, 30 ] ] }, { "plaintext": " Copper pour", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 7339924 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Antenna tuner", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 582127 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Salisbury screen", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 3508616 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Image antenna", "section_idx": 3, "section_name": "See also", "target_page_ids": [ 41251 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Groundplane antenna model FA-2 from the book PRACTICAL ANTENNA DESIGN second edition, Philippine copyright, 1990, 1994 by Elpidio C. Latorilla ", "section_idx": 4, "section_name": "References", "target_page_ids": [ 23440 ], "anchor_spans": [ [ 87, 97 ] ] }, { "plaintext": " John Whitmore, sci.electronics > What is a PCB with a Ground plane?. August 11, 1992.", "section_idx": 4, "section_name": "References", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Amateur Quarter Wave Ground Plane Antenna Calculator. Computer Support Group, Inc., 2006.", "section_idx": 4, "section_name": "References", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " What is a Ground Plane? Criterion Cellular, 2006.", "section_idx": 4, "section_name": "References", "target_page_ids": [], "anchor_spans": [] } ]

[ "Antennas", "Telecommunications_infrastructure" ]

[]

[ { "plaintext": "Ground waves are radio waves propagating parallel to and adjacent to the surface of the Earth, following the curvature of the Earth. This radiation is known as Norton surface wave, or more properly Norton ground wave, because ground waves in radio propagation are not confined to the surface. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 98132, 271195, 233636 ], "anchor_spans": [ [ 17, 28 ], [ 29, 40 ], [ 109, 131 ] ] }, { "plaintext": "Lower frequency radio waves, below 3MHz, travel efficiently as ground waves. In ITU nomenclature, this includes (in order): medium frequency (MF), low frequency (LF), very low frequency (VLF), ultra low frequency (ULF), super low frequency (SLF), extremely low frequency (ELF) waves.", "section_idx": 1, "section_name": "Overview", "target_page_ids": [ 10779, 9426, 160519, 160518, 160505, 887766, 887767, 366253 ], "anchor_spans": [ [ 6, 15 ], [ 16, 27 ], [ 124, 140 ], [ 147, 160 ], [ 167, 185 ], [ 193, 212 ], [ 220, 239 ], [ 247, 270 ] ] }, { "plaintext": "Ground propagation works because lower-frequency waves are more strongly diffracted around obstacles due to their long wavelengths, allowing them to follow the Earth's curvature. Ground waves propagate in vertical polarization, with their magnetic field horizontal and electric field (close to) vertical. ", "section_idx": 1, "section_name": "Overview", "target_page_ids": [ 8603, 33125, 233636, 41564, 36563, 41092 ], "anchor_spans": [ [ 73, 83 ], [ 119, 129 ], [ 160, 177 ], [ 205, 226 ], [ 239, 253 ], [ 269, 283 ] ] }, { "plaintext": "Conductivity of the surface affects the propagation of ground waves, with more conductive surfaces such as sea water providing better propagation. Increasing the conductivity in a surface results in less dissipation. The refractive indices are subject to spatial and temporal changes. Since the ground is not a perfect electrical conductor, ground waves are attenuated as they follow the earth's surface. The wavefronts initially are vertical, but the ground, acting as a lossy dielectric, causes the wave to tilt forward as it travels. This directs some of the energy into the earth where it is dissipated, so that the signal decreases exponentially.", "section_idx": 1, "section_name": "Overview", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Most long-distance LF \"longwave\" radio communication (between 30kHz and 300kHz) is a result of groundwave propagation. Mediumwave radio transmissions (frequencies between 300kHz and 3000kHz), including AM broadcast band, travel both as groundwaves and, for longer distances at night, as skywaves. Ground losses become lower at lower frequencies, greatly increasing the coverage of AM stations using the lower end of the band. The VLF and LF frequencies are mostly used for military communications, especially with ships and submarines. The lower the frequency the better the waves penetrate sea water. ELF waves (below 3kHz) have even been used to communicate with deeply submerged submarines.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 168741, 110381, 113509, 276281, 113509, 160505, 160518 ], "anchor_spans": [ [ 23, 31 ], [ 119, 129 ], [ 202, 214 ], [ 287, 294 ], [ 381, 392 ], [ 430, 433 ], [ 438, 440 ] ] }, { "plaintext": "Ground waves have been used in over-the-horizon radar, which operates mainly at frequencies between 2–20MHz over the sea, which has a sufficiently high conductivity to convey them to and from a reasonable distance (up to 100km or more; over-horizon radar also uses skywave propagation at much greater distances). In the development of radio, ground waves were used extensively. Early commercial and professional radio services relied exclusively on long wave, low frequencies and ground-wave propagation. To prevent interference with these services, amateur and experimental transmitters were restricted to the high frequencies (HF), felt to be useless since their ground-wave range was limited. Upon discovery of the other propagation modes possible at medium wave and short wave frequencies, the advantages of HF for commercial and military purposes became apparent. Amateur experimentation was then confined only to authorized frequencies in the range.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 1694703, 3800477, 168741, 110381, 57980 ], "anchor_spans": [ [ 31, 53 ], [ 320, 340 ], [ 449, 458 ], [ 756, 767 ], [ 772, 782 ] ] }, { "plaintext": "Mediumwave and shortwave reflect off the ionosphere at night, which is known as skywave. During daylight hours, the lower D layer of the ionosphere forms and absorbs lower frequency energy. This prevents skywave propagation from being very effective on mediumwave frequencies in daylight hours. At night, when the D layer dissipates, mediumwave transmissions travel better by skywave. Ground waves do not include ionospheric and tropospheric waves.", "section_idx": 3, "section_name": "Related terms", "target_page_ids": [ 57980, 276281, 15097, 15097, 41822 ], "anchor_spans": [ [ 15, 24 ], [ 80, 87 ], [ 122, 129 ], [ 413, 424 ], [ 429, 441 ] ] }, { "plaintext": "The propagation of sound waves through the ground taking advantage of the Earth's ability to more efficiently transmit low frequency is known as audio ground wave (AGW).", "section_idx": 3, "section_name": "Related terms", "target_page_ids": [ 160518 ], "anchor_spans": [ [ 119, 132 ] ] }, { "plaintext": "Skywave", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 276281 ], "anchor_spans": [ [ 0, 7 ] ] } ]

[ "Radio_frequency_propagation" ]

[]

[ { "plaintext": "In telecommunication, a group alerting and dispatching system is a service feature that (a) enables a controlling telephone to place a call to a specified number of telephones simultaneously, (b) enables the call to be recorded, (c) if any of the called lines is busy, enables the equipment to camp on until the busy line is free, and (d) rings the free line and plays the recorded message.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 417914, 30003, 406703, 946963, 41367 ], "anchor_spans": [ [ 3, 20 ], [ 67, 82 ], [ 114, 123 ], [ 135, 139 ], [ 317, 321 ], [ 382, 389 ] ] } ]

[ "Telephony" ]

[]

[ { "plaintext": "In signal processing, group delay and phase delay are delay times experienced by a signal's various Frequency components when the signal passes through a system that is linear time-invariant (LTI), such as a microphone, coaxial cable, amplifier, loudspeaker, telecommunications system or ethernet cable. These delays are generally frequency dependent. This means that different frequency components experience different delays, which cause distortion of the signal's waveform as it passes through the system. This distortion can cause problems such as poor fidelity in analog video and analog audio, or a high bit-error rate in a digital bit stream. For a modulation signal (passband signal), the signal intelligence is carried exclusively in the wave envelope. Group delay therefore operates only with the frequency components derived from the envelope.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 29324, 1383899, 65886, 46380, 9931, 45871, 40925, 9499, 41052, 47592, 13624, 32441, 190003, 40794, 20637, 27367275 ], "anchor_spans": [ [ 3, 20 ], [ 169, 190 ], [ 208, 218 ], [ 220, 233 ], [ 235, 244 ], [ 246, 257 ], [ 259, 284 ], [ 288, 302 ], [ 440, 450 ], [ 467, 475 ], [ 557, 565 ], [ 569, 581 ], [ 586, 598 ], [ 610, 624 ], [ 656, 673 ], [ 747, 760 ] ] }, { "plaintext": "The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a Frequency components of a signal of a time varying physical quantityfor example a voltage signalappears at the LTI system input, to the time when a copy of that same frequency componentperhaps of a different physical phenomenonappears at the LTI system output.", "section_idx": 1, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A varying phase response as a function of frequency, from which group delay and phase delay can be calculated, typically occurs in devices such as microphones, amplifiers, loudspeakers, magnetic recorders, headphones, coaxial cables, and antialiasing filters. All frequency components of a signal are delayed when passed through such devices, or when propagating through space or a medium, such as air or water. ", "section_idx": 1, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A linear time-invariant system or device has a phase response property and a phase delay property, where one can be calculated exactly from the other. Phase delay directly measures the device or system time delay of individual frequency components. If the phase delay function at any given frequencywithin a frequency range of interesthas the same constant of proportionality between the phase at a selected frequency and the selected frequency itself, the system/device will have the ideal of a flat phase delay property, a.k.a. linear phase. Since phase delay is a function of frequency giving time delay, a departure from the flatness of its function graph can reveal time delay differences among the various signal Frequency components of a signal, in which case those differences will contribute to signal distortion, which is manifested as the output signal waveform shape being different from that of the input signal. The phase delay property in general does not give useful information if the device input is a modulated signal. For that, group delay must be used.", "section_idx": 1, "section_name": "Introduction", "target_page_ids": [ 1543837, 1291180, 20637 ], "anchor_spans": [ [ 47, 61 ], [ 530, 542 ], [ 1020, 1029 ] ] }, { "plaintext": "The group delay is a convenient measure of the linearity of the phase with respect to frequency in a modulation system.", "section_idx": 1, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A device's group delay can be exactly calcuated from the device's phase response, but not the other way around.", "section_idx": 1, "section_name": "Introduction", "target_page_ids": [ 1543837 ], "anchor_spans": [ [ 66, 80 ] ] }, { "plaintext": "The simplest use case for group delay is illustrated in Figure 1 which shows a conceptual modulation system, which is itself an LTI system with a baseband output that is ideally an accurate copy of the baseband signal input. This system as a whole is referred to here as the outer LTI system/device, which contains an inner (red block) LTI system/device. As is often the case for a radio system, the inner red LTI system in Fig 1 can represent two LTI systems in cascade, for example an amplifier driving a transmitting antenna at the sending end and the other an antenna and amplifier at the receiving end.", "section_idx": 1, "section_name": "Introduction", "target_page_ids": [ 20637 ], "anchor_spans": [ [ 90, 100 ] ] }, { "plaintext": "Amplitude modulation creates the passband signal by shifting the baseband frequency components to a much higher frequency range.  Although the frequencies are different, the passband signal carries the same information as the baseband signal. The demodulator does the inverse, shifting the passband frequencies back down to the original baseband frequency range. Ideally, the output (baseband) signal is a time delayed version of the input (baseband) signal where the waveform shape of the output is identical to that of the input.", "section_idx": 1, "section_name": "Introduction", "target_page_ids": [ 1140 ], "anchor_spans": [ [ 0, 20 ] ] }, { "plaintext": "In Figure 1, the outer system phase delay is the meaningful performance metric. For amplitude modulation, the inner red LTI device group delay becomes the outer LTI device phase delay. If the inner red device group delay is completely flat in the frequency range of interest, the outer device will have the ideal of a phase delay that is also completely flat, where the contribution of distortion due to the outer LTI device’s phase responsedetermined entirely by the inner device’s possibly different phase responseis eliminated. In that case, the group delay of the inner red device and the phase delay of the outer device give the same time delay figure for the signal as a whole, from the baseband input to the baseband output. It is significant to note that it is possible for the inner (red) device to have a very non-flat phase delay (but flat group delay), while the outer device has the ideal of a perfectly flat phase delay.  This is fortunate because in LTI device design, a flat group delay is easier to achieve than a flat phase delay.", "section_idx": 1, "section_name": "Introduction", "target_page_ids": [ 1543837, 1543837 ], "anchor_spans": [ [ 427, 441 ], [ 502, 516 ] ] }, { "plaintext": "In an angle-modulation systemsuch as with frequency modulation (FM) or phase modulation (PM)the (FM or PM) passband signal applied to an LTI system input can be analyzed as two separate passband signals, an in-phase (I) amplitude modulation AM passband signal and a quadrature-phase (Q) amplitude modulation AM passband signal, where their sum exactly reconstructs the original angle-modulation (FM or PM) passband signal. While the (FM/PM) passband signal is not amplitude modulation, and therefore has no apparent outer envelope, the I and Q passband signals do indeed have amplitude modulation envelopes. (However, unlike with regular amplitude modulation, the I and Q envelopes do not resemble the wave shape of the baseband signals, even though 100 percent of the baseband signal is represented in a complex manner by their envelopes.) So, for each of the I and Q passband signals, a flat group delay ensures that neither the I pass band envelope nor the Q passband envelope will have wave shape distortion, so when the I passband signal and the Q passband signal is added back together, the sum is the original FM/PM passband signal, which will also be unaltered.", "section_idx": 1, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For a periodic signal, a frequency component is a sinusoid with properties that include time-based frequency and phase.", "section_idx": 2, "section_name": "Background", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The sinusoid, with or without a time based frequency property, is generated by a circle as shown in the figure. In this example, the sinusoid is a sine wave that is traced out using the trigonometric function.", "section_idx": 2, "section_name": "Background", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "When an increasing angle makes a complete CCW rotation around the circle, one cycle of the function’s pattern is generated. Further increasing the angle beyond 360 degrees simply rotates around the circle again, completing another cycle, where each succeeding cycle repeats the same pattern, making the function periodic. (See \"Rotating vector...\" animation on the left.) The angle value has no limit, and so the number of times the pattern repeats itself also has no limit. Because of this, a sinusoid has no beginning and no end. A sinusoidal function is based on either or both of the trigonometric functions and .", "section_idx": 2, "section_name": "Background", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In LTI system theory, control theory, and in digital or analog signal processing, the relationship between the input signal, and the output signal, , of an LTI system is governed by a convolution operation:", "section_idx": 3, "section_name": "Theory", "target_page_ids": [ 1383899, 7039, 8525, 405746, 7519 ], "anchor_spans": [ [ 3, 20 ], [ 22, 36 ], [ 45, 52 ], [ 56, 80 ], [ 185, 196 ] ] }, { "plaintext": "Or, in the frequency domain,", "section_idx": 3, "section_name": "Theory", "target_page_ids": [ 370346 ], "anchor_spans": [ [ 11, 27 ] ] }, { "plaintext": "where", "section_idx": 3, "section_name": "Theory", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "and", "section_idx": 3, "section_name": "Theory", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " .", "section_idx": 3, "section_name": "Theory", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Here is the time-domain impulse response of the LTI system and , , , are the Laplace transforms of the input , output , and impulse response , respectively. is called the transfer function of the LTI system and, like the impulse response , fully defines the input-output characteristics of the LTI system.", "section_idx": 3, "section_name": "Theory", "target_page_ids": [ 545825, 18610, 31146 ], "anchor_spans": [ [ 25, 41 ], [ 78, 95 ], [ 174, 191 ] ] }, { "plaintext": "Suppose that such a system is driven by a quasi-sinusoidal signal, such as a sinusoid having an amplitude envelope that is slowly changing relative to the frequency of the sinusoid. Mathematically, this means that the quasi-sinusoidal driving signal has the form", "section_idx": 3, "section_name": "Theory", "target_page_ids": [ 324749 ], "anchor_spans": [ [ 77, 85 ] ] }, { "plaintext": "and the slowly changing amplitude envelope means that", "section_idx": 3, "section_name": "Theory", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Then the output of such an LTI system is very well approximated as", "section_idx": 3, "section_name": "Theory", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Here is the group delay and is the phase delay, and they are given by the expressions below (and potentially are functions of the angular frequency ). The phase of the sinusoid, as indicated by the positions of the zero crossings, is delayed in time by an amount equal to the phase delay, . The envelope of the sinusoid is delayed in time by the group delay, .", "section_idx": 3, "section_name": "Theory", "target_page_ids": [ 199829 ], "anchor_spans": [ [ 132, 149 ] ] }, { "plaintext": "In a linear phase system (with non-inverting gain), both and are constant (i.e., independent of ) and equal, and their common value equals the overall delay of the system; and the unwrapped phase shift of the system (namely ) is negative, with magnitude increasing linearly with frequency .", "section_idx": 3, "section_name": "Theory", "target_page_ids": [ 1291180, 24047 ], "anchor_spans": [ [ 5, 17 ], [ 192, 203 ] ] }, { "plaintext": "More generally, it can be shown that for an LTI system with transfer function driven by a complex sinusoid of unit amplitude,", "section_idx": 3, "section_name": "Theory", "target_page_ids": [ 1256073 ], "anchor_spans": [ [ 91, 107 ] ] }, { "plaintext": "the output is", "section_idx": 3, "section_name": "Theory", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where the phase shift is", "section_idx": 3, "section_name": "Theory", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Additionally, it can be shown that the group delay, , and phase delay, , are frequency-dependent. They can be computed from the unwrapped phase shift by", "section_idx": 3, "section_name": "Theory", "target_page_ids": [ 3125808 ], "anchor_spans": [ [ 128, 137 ] ] }, { "plaintext": " .", "section_idx": 3, "section_name": "Theory", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "That is, the group delay at each frequency equals the negative of the slope of the phase at", "section_idx": 3, "section_name": "Theory", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "that frequency (compare to instantaneous frequency).", "section_idx": 3, "section_name": "Theory", "target_page_ids": [ 3125808 ], "anchor_spans": [ [ 27, 50 ] ] }, { "plaintext": "Group delay has some importance in the audio field and especially in the sound reproduction field. Many components of an audio reproduction chain, notably loudspeakers and multiway loudspeaker crossover networks, introduce group delay in the audio signal. It is therefore important to know the threshold of audibility of group delay with respect to frequency, especially if the audio chain is supposed to provide high fidelity reproduction. The best thresholds of audibility table has been provided by Blauert and Laws.", "section_idx": 4, "section_name": "Group delay in audio", "target_page_ids": [ 45871, 96692, 13624 ], "anchor_spans": [ [ 155, 167 ], [ 193, 211 ], [ 413, 426 ] ] }, { "plaintext": "Flanagan, Moore and Stone conclude that at 1, 2 and 4kHz, a group delay of about 1.6ms is audible with headphones in a non-reverberant condition. Other experimental results suggest that when the group delay in the frequency range from 300Hz to 1kHz is below 1.0ms, it is inaudible.", "section_idx": 4, "section_name": "Group delay in audio", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The waveform of an audio signal can be reproduced exactly by a system that has a flat frequency response over the bandwidth of the signal and a phase delay that is equal to the group delay. Leach introduced the concept of differential time-delay distortion, defined as the difference between the phase delay and the group delay, which is given by:", "section_idx": 4, "section_name": "Group delay in audio", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " .", "section_idx": 4, "section_name": "Group delay in audio", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "An ideal system should exhibit zero or negligible differential time-delay distortion.", "section_idx": 4, "section_name": "Group delay in audio", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "It is possible to use digital signal processing techniques to correct the group delay distortion that arises due to the use of crossover networks in multi-way loudspeaker systems. This involves considerable computational modeling of loudspeaker systems in order to successfully apply delay equalization, using the Parks-McClellan FIR equiripple filter design algorithm.", "section_idx": 4, "section_name": "Group delay in audio", "target_page_ids": [ 4882496 ], "anchor_spans": [ [ 314, 368 ] ] }, { "plaintext": "Group delay is important in physics, and in particular in optics.", "section_idx": 5, "section_name": "Group delay in optics", "target_page_ids": [ 22939, 22483 ], "anchor_spans": [ [ 28, 35 ], [ 58, 64 ] ] }, { "plaintext": "In an optical fiber, group delay is the transit time required for optical power, traveling at a given mode's group velocity, to travel a given distance. For optical fiber dispersion measurement purposes, the quantity of interest is group delay per unit length, which is the reciprocal of the group velocity of a particular mode. The measured group delay of a signal through an optical fiber exhibits a wavelength dependence due to the various dispersion mechanisms present in the fiber.", "section_idx": 5, "section_name": "Group delay in optics", "target_page_ids": [ 3372377, 30012, 24236, 516150, 12778, 172333, 1275395, 41703, 33125, 172333 ], "anchor_spans": [ [ 6, 19 ], [ 48, 52 ], [ 74, 79 ], [ 102, 106 ], [ 109, 123 ], [ 171, 181 ], [ 238, 243 ], [ 359, 365 ], [ 402, 412 ], [ 443, 453 ] ] }, { "plaintext": "It is often desirable for the group delay to be constant across all frequencies; otherwise there is temporal smearing of the signal. Because group delay is , it therefore follows that a constant group delay can be achieved if the transfer function of the device or medium has a linear phase response (i.e., where the group delay is a constant). The degree of nonlinearity of the phase indicates the deviation of the group delay from a constant value.", "section_idx": 5, "section_name": "Group delay in optics", "target_page_ids": [ 31146, 91591 ], "anchor_spans": [ [ 230, 247 ], [ 278, 284 ] ] }, { "plaintext": "A transmitting apparatus is said to have true time delay (TTD) if the time delay is independent of the frequency of the electrical signal. TTD is an important characteristic of lossless and low-loss, dispersion free, transmission lines. TTD allows for a wide instantaneous signal bandwidth with virtually no signal distortion such as pulse broadening during pulsed operation.", "section_idx": 6, "section_name": "True time delay", "target_page_ids": [ 10779, 3967 ], "anchor_spans": [ [ 103, 112 ], [ 280, 289 ] ] }, { "plaintext": " Audio system measurements", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 302052 ], "anchor_spans": [ [ 1, 26 ] ] }, { "plaintext": " Bessel filter", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 2071179 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Eye pattern", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 41131 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Group velocity — \"The group velocity of light in a medium is the inverse of the group delay per unit length.\"", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 12778 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Discussion of Group Delay in Loudspeakers", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Group Delay Explanations and Applications", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " \"Introduction to Digital Filters with Audio Applications\", Julius O. Smith III, (September 2007 Edition).", "section_idx": 9, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Optics", "Waves", "Signal_processing", "Electrical_engineering" ]

[]

[ { "plaintext": "A guided ray (also bound ray or trapped ray) is a ray of light in a multi-mode optical fiber, which is confined by the core.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 3364761, 2940457, 3372377 ], "anchor_spans": [ [ 50, 53 ], [ 68, 92 ], [ 119, 123 ] ] }, { "plaintext": "For step index fiber, light entering the fiber will be guided if it falls within the acceptance cone of the fiber, that is if it makes an angle with the fiber axis that is less than the acceptance angle,", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41748 ], "anchor_spans": [ [ 4, 20 ] ] }, { "plaintext": " ,", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "where", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "θ is the angle the ray makes with the fiber axis, before entering the fiber,", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "n0 is the refractive index along the central axis (core) of the fiber, and", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 25880 ], "anchor_spans": [ [ 10, 26 ] ] }, { "plaintext": "nc is the refractive index of the cladding.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The quantity is the numerical aperture of the fiber. The quantity is sometimes called the total acceptance angle of the fiber.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41432 ], "anchor_spans": [ [ 21, 39 ] ] }, { "plaintext": "This result can be derived from Snell's law by considering the critical angle. Light that enters the core with an angle below the acceptance angle strikes the core-cladding boundary at an angle above the critical angle, and experiences total internal reflection. This repeats on every bounce within the fiber core, and so the light is confined to the core. The confinement of light by the fiber can also be described in terms of bound modes or guided modes. This treatment is necessary when considering singlemode fiber, since the ray model does not accurately describe the propagation of light in this type of fiber.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 42964, 30426, 30426, 41716 ], "anchor_spans": [ [ 32, 43 ], [ 63, 77 ], [ 236, 261 ], [ 503, 519 ] ] }, { "plaintext": "Numerical aperture", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 41432 ], "anchor_spans": [ [ 0, 18 ] ] }, { "plaintext": "Acceptance angle (solar concentrator), same construct for another use", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 31633769 ], "anchor_spans": [ [ 0, 37 ] ] }, { "plaintext": " Federal Standard 1037C", "section_idx": 2, "section_name": "References", "target_page_ids": [], "anchor_spans": [] } ]

[ "Fiber_optics" ]

[]

[ { "plaintext": "In telecommunication, a Hagelbarger code is a convolutional code that enables error bursts to be corrected provided that there are relatively long error-free intervals between the error bursts. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 40962, 41119 ], "anchor_spans": [ [ 3, 20 ], [ 46, 64 ], [ 78, 89 ] ] }, { "plaintext": "In the Hagelbarger code, inserted parity check bits are spread out in time so that an error burst is not likely to affect more than one of the groups in which parity is checked.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10375, 30012 ], "anchor_spans": [ [ 34, 46 ], [ 70, 74 ] ] } ]

[ "Error_detection_and_correction" ]

[]

[ { "plaintext": "In a facsimile system the halftone characteristic is either:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10826 ], "anchor_spans": [ [ 5, 14 ] ] }, { "plaintext": " the relationship between the density of the recorded copy and the density of the original, or", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 14632149 ], "anchor_spans": [ [ 54, 58 ] ] }, { "plaintext": " the relationship between the amplitude of the facsimile signal to either the density of the object or the density of the recorded copy when only a portion of the system is under consideration. In an FM facsimile system, an appropriate parameter other than the amplitude is used.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41703, 8286675 ], "anchor_spans": [ [ 57, 63 ], [ 163, 169 ] ] }, { "plaintext": "Halftone", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 61625 ], "anchor_spans": [ [ 0, 8 ] ] } ]

[ "Fax" ]

[]

[ { "plaintext": "In computer science and telecommunication, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are perfect codes, that is, they achieve the highest possible rate for codes with their block length and minimum distance of three.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 5323, 33094374, 1866743, 194467, 1879428, 1134659, 1134659, 1134659 ], "anchor_spans": [ [ 3, 19 ], [ 24, 41 ], [ 73, 102 ], [ 248, 259 ], [ 353, 365 ], [ 411, 415 ], [ 437, 449 ], [ 454, 470 ] ] }, { "plaintext": "Richard W. Hamming invented Hamming codes in 1950 as a way of automatically correcting errors introduced by punched card readers. In his original paper, Hamming elaborated his general idea, but specifically focused on the Hamming(7,4) code which adds three parity bits to four bits of data.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 99326, 24420, 8712675 ], "anchor_spans": [ [ 0, 18 ], [ 108, 120 ], [ 222, 234 ] ] }, { "plaintext": "In mathematical terms, Hamming codes are a class of binary linear code. For each integer there is a code-word with block length and message length . Hence the rate of Hamming codes is , which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from any code word to any other code word is three) and block length . The parity-check matrix of a Hamming code is constructed by listing all columns of length that are non-zero, which means that the dual code of the Hamming code is the shortened Hadamard code. The parity-check matrix has the property that any two columns are pairwise linearly independent.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 18831, 1134659, 1134659, 10557570, 1864548, 7428961, 101863 ], "anchor_spans": [ [ 3, 15 ], [ 116, 128 ], [ 134, 148 ], [ 388, 407 ], [ 515, 524 ], [ 552, 575 ], [ 652, 672 ] ] }, { "plaintext": "Due to the limited redundancy that Hamming codes add to the data, they can only detect and correct errors when the error rate is low. This is the case in computer memory (usually RAM), where bit errors are extremely rare and Hamming codes are widely used, and a RAM with this correction system is a ECC RAM (ECC memory). In this context, an extended Hamming code having one extra parity bit is often used. Extended Hamming codes achieve a Hamming distance of four, which allows the decoder to distinguish between when at most one one-bit error occurs and when any two-bit errors occur. In this sense, extended Hamming codes are single-error correcting and double-error detecting, abbreviated as SECDED.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 4473248 ], "anchor_spans": [ [ 308, 318 ] ] }, { "plaintext": "Richard Hamming, the inventor of Hamming codes, worked at Bell Labs in the late 1940s on the Bell Model V computer, an electromechanical relay-based machine with cycle times in seconds. Input was fed in on punched paper tape, seven-eighths of an inch wide, which had up to six holes per row. During weekdays, when errors in the relays were detected, the machine would stop and flash lights so that the operators could correct the problem. During after-hours periods and on weekends, when there were no operators, the machine simply moved on to the next job.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 99326, 3712, 58340340, 31322120, 49761 ], "anchor_spans": [ [ 0, 15 ], [ 58, 67 ], [ 98, 105 ], [ 119, 136 ], [ 206, 224 ] ] }, { "plaintext": "Hamming worked on weekends, and grew increasingly frustrated with having to restart his programs from scratch due to detected errors. In a taped interview, Hamming said, \"And so I said, 'Damn it, if the machine can detect an error, why can't it locate the position of the error and correct it?'\". Over the next few years, he worked on the problem of error-correction, developing an increasingly powerful array of algorithms. In 1950, he published what is now known as Hamming code, which remains in use today in applications such as ECC memory.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 4473248 ], "anchor_spans": [ [ 533, 543 ] ] }, { "plaintext": "A number of simple error-detecting codes were used before Hamming codes, but none were as effective as Hamming codes in the same overhead of space.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Parity adds a single bit that indicates whether the number of ones (bit-positions with values of one) in the preceding data was even or odd. If an odd number of bits is changed in transmission, the message will change parity and the error can be detected at this point; however, the bit that changed may have been the parity bit itself. The most common convention is that a parity value of one indicates that there is an odd number of ones in the data, and a parity value of zero indicates that there is an even number of ones. If the number of bits changed is even, the check bit will be valid and the error will not be detected.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 3364, 143135, 143135 ], "anchor_spans": [ [ 21, 24 ], [ 128, 132 ], [ 136, 139 ] ] }, { "plaintext": "Moreover, parity does not indicate which bit contained the error, even when it can detect it. The data must be discarded entirely and re-transmitted from scratch. On a noisy transmission medium, a successful transmission could take a long time or may never occur. However, while the quality of parity checking is poor, since it uses only a single bit, this method results in the least overhead.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A two-out-of-five code is an encoding scheme which uses five bits consisting of exactly three 0s and two 1s. This provides ten possible combinations, enough to represent the digits 0–9. This scheme can detect all single bit-errors, all odd numbered bit-errors and some even numbered bit-errors (for example the flipping of both 1-bits). However it still cannot correct any of these errors.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Another code in use at the time repeated every data bit multiple times in order to ensure that it was sent correctly. For instance, if the data bit to be sent is a 1, an repetition code will send 111. If the three bits received are not identical, an error occurred during transmission. If the channel is clean enough, most of the time only one bit will change in each triple. Therefore, 001, 010, and 100 each correspond to a 0 bit, while 110, 101, and 011 correspond to a 1 bit, with the greater quantity of digits that are the same ('0' or a '1') indicating what the data bit should be. A code with this ability to reconstruct the original message in the presence of errors is known as an error-correcting code. This triple repetition code is a Hamming code with since there are two parity bits, and data bit.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 3473949 ], "anchor_spans": [ [ 171, 186 ] ] }, { "plaintext": "Such codes cannot correctly repair all errors, however. In our example, if the channel flips two bits and the receiver gets 001, the system will detect the error, but conclude that the original bit is 0, which is incorrect. If we increase the size of the bit string to four, we can detect all two-bit errors but cannot correct them (the quantity of parity bits is even); at five bits, we can both detect and correct all two-bit errors, but not all three-bit errors.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Moreover, increasing the size of the parity bit string is inefficient, reducing throughput by three times in our original case, and the efficiency drops drastically as we increase the number of times each bit is duplicated in order to detect and correct more errors.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "If more error-correcting bits are included with a message, and if those bits can be arranged such that different incorrect bits produce different error results, then bad bits could be identified. In a seven-bit message, there are seven possible single bit errors, so three error control bits could potentially specify not only that an error occurred but also which bit caused the error.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Hamming studied the existing coding schemes, including two-of-five, and generalized their concepts. To start with, he developed a nomenclature to describe the system, including the number of data bits and error-correction bits in a block. For instance, parity includes a single bit for any data word, so assuming ASCII words with seven bits, Hamming described this as an (8,7) code, with eight bits in total, of which seven are data. The repetition example would be (3,1), following the same logic. The code rate is the second number divided by the first, for our repetition example, 1/3.", "section_idx": 2, "section_name": "Description", "target_page_ids": [ 586, 7981806 ], "anchor_spans": [ [ 313, 318 ], [ 503, 512 ] ] }, { "plaintext": "Hamming also noticed the problems with flipping two or more bits, and described this as the \"distance\" (it is now called the Hamming distance, after him). Parity has a distance of 2, so one bit flip can be detected but not corrected, and any two bit flips will be invisible. The (3,1) repetition has a distance of 3, as three bits need to be flipped in the same triple to obtain another code word with no visible errors. It can correct one-bit errors or it can detect - but not correct - two-bit errors. A (4,1) repetition (each bit is repeated four times) has a distance of 4, so flipping three bits can be detected, but not corrected. When three bits flip in the same group there can be situations where attempting to correct will produce the wrong code word. In general, a code with distance k can detect but not correct errors.", "section_idx": 2, "section_name": "Description", "target_page_ids": [ 41227 ], "anchor_spans": [ [ 125, 141 ] ] }, { "plaintext": "Hamming was interested in two problems at once: increasing the distance as much as possible, while at the same time increasing the code rate as much as possible. During the 1940s he developed several encoding schemes that were dramatic improvements on existing codes. The key to all of his systems was to have the parity bits overlap, such that they managed to check each other as well as the data.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The following general algorithm generates a single-error correcting (SEC) code for any number of bits. The main idea is to choose the error-correcting bits such that the index-XOR (the XOR of all the bit positions containing a 1) is 0. We use positions 1, 10, 100, etc. (in binary) as the error-correcting bits, which guarantees it is possible to set the error-correcting bits so that the index-XOR of the whole message is 0. If the receiver receives a string with index-XOR 0, they can conclude there were no corruptions, and otherwise, the index-XOR indicates the index of the corrupted bit.", "section_idx": 2, "section_name": "Description", "target_page_ids": [ 105979 ], "anchor_spans": [ [ 185, 188 ] ] }, { "plaintext": "An algorithm can be deduced from the following description:", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Number the bits starting from 1: bit 1, 2, 3, 4, 5, 6, 7, etc.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Write the bit numbers in binary: 1, 10, 11, 100, 101, 110, 111, etc.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " All bit positions that are powers of two (have a single 1 bit in the binary form of their position) are parity bits: 1, 2, 4, 8, etc. (1, 10, 100, 1000)", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " All other bit positions, with two or more 1 bits in the binary form of their position, are data bits.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Each data bit is included in a unique set of 2 or more parity bits, as determined by the binary form of its bit position.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Parity bit 1 covers all bit positions which have the least significant bit set: bit 1 (the parity bit itself), 3, 5, 7, 9, etc.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Parity bit 2 covers all bit positions which have the second least significant bit set: bits 2-3, 6-7, 10-11, etc.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Parity bit 4 covers all bit positions which have the third least significant bit set: bits 4–7, 12–15, 20–23, etc.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Parity bit 8 covers all bit positions which have the fourth least significant bit set: bits 8–15, 24–31, 40–47, etc.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " In general each parity bit covers all bits where the bitwise AND of the parity position and the bit position is non-zero.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "If a byte of data to be encoded is 10011010, then the data word (using _ to represent the parity bits) would be __1_001_1010, and the code word is 011100101010.", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The choice of the parity, even or odd, is irrelevant but the same choice must be used for both encoding and decoding. ", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "This general rule can be shown visually:", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "{| class=\"wikitable\" style=\"text-align:center;\"", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|-", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!colspan=\"2\"| ", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! ", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|rowspan=\"7\"| ", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|-", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!colspan=\"2\"| Encoded data bits", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p1", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p2 !! d1", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p4 !! d2 !! d3 !! d4", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p8 !! d5 !! d6 !! d7 !! d8 !! d9 !! d10 !! d11", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p16 !! d12 !! d13 !! d14 !! d15", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|-", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!rowspan=\"5\"|Paritybitcoverage", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p1", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| || || || || || || || || || || || || || || || || || || || ", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|-", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p2", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| || || || || || || || || || || || || || || || || || || || ", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|-", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p4", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| || || || || || || || || || || || || || || || || || || || ", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|-", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p8", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| || || || || || || || || || || || || || || || || || || || ", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|-", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "!style=\"background-color: #90FF90;\"| p16", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "| || || || || || || || || || || || || || || || || || || || ", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "|}", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Shown are only 20 encoded bits (5 parity, 15 data) but the pattern continues indefinitely. The key thing about Hamming Codes that can be seen from visual inspection is that any given bit is included in a unique set of parity bits. To check for errors, check all of the parity bits. The pattern of errors, called the error syndrome, identifies the bit in error. If all parity bits are correct, there is no error. Otherwise, the sum of the positions of the erroneous parity bits identifies the erroneous bit. For example, if the parity bits in positions 1, 2 and 8 indicate an error, then bit 1+2+8=11 is in error. If only one parity bit indicates an error, the parity bit itself is in error.", "section_idx": 2, "section_name": "Description", "target_page_ids": [ 1940782 ], "anchor_spans": [ [ 319, 333 ] ] }, { "plaintext": "With parity bits, bits from 1 up to can be covered. After discounting the parity bits, bits remain for use as data. As varies, we get all the possible Hamming codes:", "section_idx": 2, "section_name": "Description", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Hamming codes have a minimum distance of 3, which means that the decoder can detect and correct a single error, but it cannot distinguish a double bit error of some codeword from a single bit error of a different codeword. Thus, some double-bit errors will be incorrectly decoded as if they were single bit errors and therefore go undetected, unless no correction is attempted.", "section_idx": 3, "section_name": "Hamming codes with additional parity (SECDED)", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "To remedy this shortcoming, Hamming codes can be extended by an extra parity bit. This way, it is possible to increase the minimum distance of the Hamming code to 4, which allows the decoder to distinguish between single bit errors and two-bit errors. Thus the decoder can detect and correct a single error and at the same time detect (but not correct) a double error.", "section_idx": 3, "section_name": "Hamming codes with additional parity (SECDED)", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "If the decoder does not attempt to correct errors, it can reliably detect triple bit errors. If the decoder does correct errors, some triple errors will be mistaken for single errors and \"corrected\" to the wrong value. Error correction is therefore a trade-off between certainty (the ability to reliably detect triple bit errors) and resiliency (the ability to keep functioning in the face of single bit errors).", "section_idx": 3, "section_name": "Hamming codes with additional parity (SECDED)", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "This extended Hamming code is popular in computer memory systems , where it is known as SECDED (abbreviated from single error correction, double error detection) . Particularly popular is the (72,64) code, a truncated (127,120) Hamming code plus an additional parity bit , which has the same space overhead as a (9,8) parity code.", "section_idx": 3, "section_name": "Hamming codes with additional parity (SECDED)", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "In 1950, Hamming introduced the [7,4] Hamming code. It encodes four data bits into seven bits by adding three parity bits. It can detect and correct single-bit errors. With the addition of an overall parity bit, it can also detect (but not correct) double-bit errors.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The matrix ", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " is called a (canonical) generator matrix of a linear (n,k) code,", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "and is called a parity-check matrix.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [ 10557570 ], "anchor_spans": [ [ 17, 36 ] ] }, { "plaintext": "This is the construction of G and H in standard (or systematic) form. Regardless of form, G and H for linear block codes must satisfy", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": ", an all-zeros matrix.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Since [7,4,3] =[n,k,d] =[2m−1, 2m−1−m,3]. The parity-check matrix H of a Hamming code is constructed by listing all columns of length m that are pair-wise independent.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [ 10557570 ], "anchor_spans": [ [ 46, 65 ] ] }, { "plaintext": "Thus H is a matrix whose left side is all of the nonzero n-tuples where order of the n-tuples in the columns of matrix does not matter. The right hand side is just the (n−k)-identity matrix.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [ 59718 ], "anchor_spans": [ [ 174, 189 ] ] }, { "plaintext": "So G can be obtained from H by taking the transpose of the left hand side of H with the identity k-identity matrix on the left hand side ofG.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [ 59718 ], "anchor_spans": [ [ 99, 114 ] ] }, { "plaintext": "The code generator matrix and the parity-check matrix are:", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [ 6133005, 10557570 ], "anchor_spans": [ [ 9, 25 ], [ 35, 54 ] ] }, { "plaintext": "and", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Finally, these matrices can be mutated into equivalent non-systematic codes by the following operations:", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Column permutations (swapping columns)", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Elementary row operations (replacing a row with a linear combination of rows)", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Example", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "From the above matrix we have 2k = 24 = 16 codewords.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Let be a row vector of binary data bits, . The codeword for any of the 16 possible data vectors is given by the standard matrix product where the summing operation is done modulo-2.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For example, let . Using the generator matrix from above, we have (after applying modulo 2, to the sum),", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The [7,4] Hamming code can easily be extended to an [8,4] code by adding an extra parity bit on top of the (7,4) encoded word (see Hamming(7,4)).", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [ 8712675 ], "anchor_spans": [ [ 131, 143 ] ] }, { "plaintext": "This can be summed up with the revised matrices:", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "and", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Note that H is not in standard form. To obtain G, elementary row operations can be used to obtain an equivalent matrix to H in systematic form:", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For example, the first row in this matrix is the sum of the second and third rows of H in non-systematic form. Using the systematic construction for Hamming codes from above, the matrix A is apparent and the systematic form of G is written as", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The non-systematic form of G can be row reduced (using elementary row operations) to match this matrix.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The addition of the fourth row effectively computes the sum of all the codeword bits (data and parity) as the fourth parity bit.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For example, is encoded (using the non-systematic form of G at the start of this section) into where blue digits are data; red digits are parity bits from the [7,4] Hamming code; and the green digit is the parity bit added by the [8,4] code.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The green digit makes the parity of the [7,4] codewords even.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Finally, it can be shown that the minimum distance has increased from 3, in the [7,4] code, to 4 in the [8,4] code. Therefore, the code can be defined as [8,4] Hamming code. ", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "To decode the [8,4] Hamming code, first check the parity bit. If the parity bit indicates an error, single error correction (the [7,4] Hamming code) will indicate the error location, with \"no error\" indicating the parity bit. If the parity bit is correct, then single error correction will indicate the (bitwise) exclusive-or of two error locations. If the locations are equal (\"no error\") then a double bit error either has not occurred, or has cancelled itself out. Otherwise, a double bit error has occurred.", "section_idx": 4, "section_name": "[7,4] Hamming code", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Coding theory", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 321869 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Golay code", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 48846980 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Reed–Muller code", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 2032752 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Reed–Solomon error correction", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 45600 ], "anchor_spans": [ [ 1, 30 ] ] }, { "plaintext": " Turbo code", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 497535 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Low-density parity-check code", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 516393 ], "anchor_spans": [ [ 1, 30 ] ] }, { "plaintext": " Hamming bound", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 1879428 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Hamming distance", "section_idx": 5, "section_name": "See also", "target_page_ids": [ 41227 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Visual Explanation of Hamming Codes", "section_idx": 8, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " CGI script for calculating Hamming distances (from R. Tervo, UNB, Canada)", "section_idx": 8, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Tool for calculating Hamming code", "section_idx": 8, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "American_inventions", "Coding_theory", "Error_detection_and_correction", "Computer_arithmetic", "1951_in_computing" ]

[]

[ { "plaintext": "In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other, or the minimum number of errors that could have transformed one string into the other. In a more general context, the Hamming distance is one of several string metrics for measuring the edit distance between two sequences. It is named after the American mathematician Richard Hamming.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 14773, 27701, 37673, 9809306, 406427, 99326 ], "anchor_spans": [ [ 3, 21 ], [ 56, 62 ], [ 134, 140 ], [ 420, 433 ], [ 453, 466 ], [ 535, 550 ] ] }, { "plaintext": "A major application is in coding theory, more specifically to block codes, in which the equal-length strings are vectors over a finite field.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 321869, 1134659, 32370, 11615 ], "anchor_spans": [ [ 26, 39 ], [ 62, 72 ], [ 113, 120 ], [ 128, 140 ] ] }, { "plaintext": "The Hamming distance between two equal-length strings of symbols is the number of positions at which the corresponding symbols are different.", "section_idx": 1, "section_name": "Definition", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The symbols may be letters, bits, or decimal digits, among other possibilities. For example, the Hamming distance between:", "section_idx": 2, "section_name": "Examples", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " \"kain\" and \"kain\" is 3.", "section_idx": 2, "section_name": "Examples", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " \"krin\" and \"krin\" is 3.", "section_idx": 2, "section_name": "Examples", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " \"kin\" and \"kin\" is 4.", "section_idx": 2, "section_name": "Examples", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " and is 4.", "section_idx": 2, "section_name": "Examples", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " 2396 and 2396 is 3.", "section_idx": 2, "section_name": "Examples", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "For a fixed length n, the Hamming distance is a metric on the set of the words of length n (also known as a Hamming space), as it fulfills the conditions of non-negativity, symmetry, the Hamming distance of two words is 0 if and only if the two words are identical, and it satisfies the triangle inequality as well: Indeed, if we fix three words a, b and c, then whenever there is a difference between the ith letter of a and the ith letter of c, then there must be a difference between the ith letter of a and ith letter of b, or between the ith letter of b and the ith letter of c. Hence the Hamming distance between a and c is not larger than the sum of the Hamming distances between a and b and between b and c. The Hamming distance between two words a and b can also be seen as the Hamming weight of a b for an appropriate choice of the operator, much as the difference between two integers can be seen as a distance from zero on the number line.", "section_idx": 3, "section_name": "Properties", "target_page_ids": [ 20018, 10939, 4566542, 53941, 1127884 ], "anchor_spans": [ [ 48, 54 ], [ 73, 77 ], [ 108, 121 ], [ 287, 306 ], [ 787, 801 ] ] }, { "plaintext": "For binary strings a and b the Hamming distance is equal to the number of ones (population count) in a XOR b. The metric space of length-n binary strings, with the Hamming distance, is known as the Hamming cube; it is equivalent as a metric space to the set of distances between vertices in a hypercube graph. One can also view a binary string of length n as a vector in by treating each symbol in the string as a real coordinate; with this embedding, the strings form the vertices of an n-dimensional hypercube, and the Hamming distance of the strings is equivalent to the Manhattan distance between the vertices.", "section_idx": 3, "section_name": "Properties", "target_page_ids": [ 1127884, 105979, 6706815, 39783, 408354 ], "anchor_spans": [ [ 80, 96 ], [ 103, 106 ], [ 293, 308 ], [ 503, 512 ], [ 575, 593 ] ] }, { "plaintext": "The minimum Hamming distance is used to define some essential notions in coding theory, such as error detecting and error correcting codes. In particular, a code C is said to be k error detecting if, and only if, the minimum Hamming distance between any two of its codewords is at least k+1.", "section_idx": 4, "section_name": "Error detection and error correction", "target_page_ids": [ 321869, 10375, 4566542 ], "anchor_spans": [ [ 73, 86 ], [ 96, 138 ], [ 157, 161 ] ] }, { "plaintext": "For example, consider the code consisting of two codewords \"000\" and \"111\". The hamming distance between these two words is 3, and therefore it is k=2 error detecting. This means that if one bit is flipped or two bits are flipped, the error can be detected. If three bits are flipped, then \"000\" becomes \"111\" and the error can not be detected.", "section_idx": 4, "section_name": "Error detection and error correction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A code C is said to be k-error correcting if, for every word w in the underlying Hamming space H, there exists at most one codeword c (from C) such that the Hamming distance between w and c is at most k. In other words, a code is k-errors correcting if, and only if, the minimum Hamming distance between any two of its codewords is at least 2k+1. This is more easily understood geometrically as any closed balls of radius k centered on distinct codewords being disjoint. These balls are also called Hamming spheres in this context.", "section_idx": 4, "section_name": "Error detection and error correction", "target_page_ids": [ 160556, 368621 ], "anchor_spans": [ [ 399, 411 ], [ 499, 513 ] ] }, { "plaintext": "For example, consider the same 3 bit code consisting of two codewords \"000\" and \"111\". The Hamming space consists of 8 words 000, 001, 010, 011, 100, 101, 110 and 111. The codeword \"000\" and the single bit error words \"001\",\"010\",\"100\" are all less than or equal to the Hamming distance of 1 to \"000\". Likewise, codeword \"111\" and its single bit error words \"110\",\"101\" and \"011\" are all within 1 Hamming distance of the original \"111\". In this code, a single bit error is always within 1 Hamming distance of the original codes, and the code can be 1-error correcting, that is k=1. The minimum Hamming distance between \"000\" and \"111\" is 3, which satisfies 2k+1 = 3.", "section_idx": 4, "section_name": "Error detection and error correction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Thus a code with minimum Hamming distance d between its codewords can detect at most d-1 errors and can correct ⌊(d-1)/2⌋ errors. The latter number is also called the packing radius or the error-correcting capability of the code.", "section_idx": 4, "section_name": "Error detection and error correction", "target_page_ids": [ 368621 ], "anchor_spans": [ [ 167, 181 ] ] }, { "plaintext": "The Hamming distance is named after Richard Hamming, who introduced the concept in his fundamental paper on Hamming codes, Error detecting and error correcting codes, in 1950. Hamming weight analysis of bits is used in several disciplines including information theory, coding theory, and cryptography.", "section_idx": 5, "section_name": "History and applications", "target_page_ids": [ 99326, 41226, 14773, 321869, 18934432 ], "anchor_spans": [ [ 36, 51 ], [ 108, 120 ], [ 249, 267 ], [ 269, 282 ], [ 288, 300 ] ] }, { "plaintext": "It is used in telecommunication to count the number of flipped bits in a fixed-length binary word as an estimate of error, and therefore is sometimes called the signal distance. For q-ary strings over an alphabet of size q≥2 the Hamming distance is applied in case of the q-ary symmetric channel, while the Lee distance is used for phase-shift keying or more generally channels susceptible to synchronization errors because the Lee distance accounts for errors of ±1. If or both distances coincide because any pair of elements from or differ by 1, but the distances are different for larger .", "section_idx": 5, "section_name": "History and applications", "target_page_ids": [ 33094374, 670, 74361, 17766039, 41551 ], "anchor_spans": [ [ 14, 31 ], [ 204, 212 ], [ 272, 295 ], [ 307, 319 ], [ 332, 350 ] ] }, { "plaintext": "The Hamming distance is also used in systematics as a measure of genetic distance.", "section_idx": 5, "section_name": "History and applications", "target_page_ids": [ 27813 ], "anchor_spans": [ [ 37, 48 ] ] }, { "plaintext": "However, for comparing strings of different lengths, or strings where not just substitutions but also insertions or deletions have to be expected, a more sophisticated metric like the Levenshtein distance is more appropriate.", "section_idx": 5, "section_name": "History and applications", "target_page_ids": [ 406418 ], "anchor_spans": [ [ 184, 204 ] ] }, { "plaintext": "The following function, written in Python 3, returns the Hamming distance between two strings:", "section_idx": 6, "section_name": "Algorithm example", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Or, in a shorter expression:", "section_idx": 6, "section_name": "Algorithm example", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The function , implemented in Python 2.3+, computes the Hamming distance between", "section_idx": 6, "section_name": "Algorithm example", "target_page_ids": [ 23862 ], "anchor_spans": [ [ 30, 41 ] ] }, { "plaintext": "two strings (or other iterable objects) of equal length by creating a sequence of Boolean values indicating mismatches and matches between corresponding positions in the two inputs and then summing the sequence with False and True values being interpreted as zero and one.", "section_idx": 6, "section_name": "Algorithm example", "target_page_ids": [ 172640 ], "anchor_spans": [ [ 22, 30 ] ] }, { "plaintext": "where the zip() function merges two equal-length collections in pairs.", "section_idx": 6, "section_name": "Algorithm example", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The following C function will compute the Hamming distance of two integers (considered as binary values, that is, as sequences of bits). The running time of this procedure is proportional to the Hamming distance rather than to the number of bits in the inputs. It computes the bitwise exclusive or of the two inputs, and then finds the Hamming weight of the result (the number of nonzero bits) using an algorithm of that repeatedly finds and clears the lowest-order nonzero bit. Some compilers support the __builtin_popcount function which can calculate this using specialized processor hardware where available.", "section_idx": 6, "section_name": "Algorithm example", "target_page_ids": [ 6021, 264399, 105979, 1127884, 1127884 ], "anchor_spans": [ [ 14, 15 ], [ 277, 284 ], [ 285, 297 ], [ 336, 350 ], [ 508, 526 ] ] }, { "plaintext": "A faster alternative is to use the population count (popcount) assembly instruction. Certain compilers such as GCC and Clang make it available via an intrinsic function:", "section_idx": 6, "section_name": "Algorithm example", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Closest string", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 19944005 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Damerau–Levenshtein distance", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 3417630 ], "anchor_spans": [ [ 1, 29 ] ] }, { "plaintext": " Euclidean distance", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 53932 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Gap-Hamming problem", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 61009235 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": " Gray code", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 50564 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " Jaccard index", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 2203756 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Levenshtein distance", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 406418 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Mahalanobis distance", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 799760 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Mannheim distance", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 17766039 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Sørensen similarity index", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 9701718 ], "anchor_spans": [ [ 1, 26 ] ] }, { "plaintext": " Sparse distributed memory", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 33547203 ], "anchor_spans": [ [ 1, 26 ] ] }, { "plaintext": " Word ladder", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 2688352 ], "anchor_spans": [ [ 1, 12 ] ] } ]

[ "String_metrics", "Coding_theory", "Articles_with_example_Python_(programming_language)_code", "Articles_with_example_C++_code", "Metric_geometry", "Cubes" ]

[]

[ { "plaintext": "In computing, a handshake is a signal between two devices or programs, used to, e.g., authenticate, coordinate. An example is the handshaking between a hypervisor and an application in a guest virtual machine.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 1267216, 9774359, 32353 ], "anchor_spans": [ [ 152, 162 ], [ 187, 192 ], [ 193, 208 ] ] }, { "plaintext": "In telecommunications, a handshake is an automated process of negotiation between two participants (example \"Alice and Bob\") through the exchange of information that establishes the protocols of a communication link at the start of the communication, before full communication begins. The handshaking process usually takes place in order to establish rules for communication when a computer attempts to communicate with another device. Signals are usually exchanged between two devices to establish a communication link. For example, when a computer communicates with another device such as a modem, the two devices will signal each other that they are switched on and ready to work, as well as to agree to which protocols are being used.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374, 679079, 7878457, 20647197 ], "anchor_spans": [ [ 3, 21 ], [ 109, 122 ], [ 382, 390 ], [ 593, 598 ] ] }, { "plaintext": "Handshaking can negotiate parameters that are acceptable to equipment and systems at both ends of the communication channel, including information transfer rate, coding alphabet, parity, interrupt procedure, and other protocol or hardware features.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 272290, 670, 194467, 15289, 28030850 ], "anchor_spans": [ [ 135, 160 ], [ 169, 177 ], [ 179, 185 ], [ 187, 196 ], [ 218, 226 ] ] }, { "plaintext": "Handshaking is a technique of communication between two entities. However, within TCP/IP RFCs, the term \"handshake\" is most commonly used to reference the TCP three-way handshake. For example, the term \"handshake\" is not present in RFCs covering FTP or SMTP. One exception is Transport Layer Security, TLS, setup, FTP RFC 4217. In place of the term \"handshake\", FTP RFC 3659 substitutes the term \"conversation\" for the passing of commands.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "A simple handshaking protocol might only involve the receiver sending a message meaning \"I received your last message and I am ready for you to send me another one.\" A more complex handshaking protocol might allow the sender to ask the receiver if it is ready to receive or for the receiver to reply with a negative acknowledgement meaning \"I did not receive your last message correctly, please resend it\" (e.g., if the data was corrupted en route).", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Handshaking facilitates connecting relatively heterogeneous systems or equipment over a communication channel without the need for human intervention to set parameters.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Establishing a normal TCP connection requires three separate steps:", "section_idx": 1, "section_name": "Example", "target_page_ids": [ 30538 ], "anchor_spans": [ [ 22, 25 ] ] }, { "plaintext": " The first host (Alice) sends the second host (Bob) a \"synchronize\" (SYN) message with its own sequence number , which Bob receives.", "section_idx": 1, "section_name": "Example", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Bob replies with a synchronize-acknowledgment (SYN-ACK) message with its own sequence number and acknowledgement number , which Alice receives.", "section_idx": 1, "section_name": "Example", "target_page_ids": [ 30538 ], "anchor_spans": [ [ 48, 55 ] ] }, { "plaintext": " Alice replies with an acknowledgment (ACK) message with acknowledgement number , which Bob receives and to which he doesn't need to reply.", "section_idx": 1, "section_name": "Example", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " In this setup, the synchronize messages act as service requests from one server to the other, while the acknowledgement messages return to the requesting server to let it know the message was received.", "section_idx": 1, "section_name": "Example", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The reason for the client and server not using a default sequence number such as 0 for establishing the connection is to protect against two incarnations of the same connection reusing the same sequence number too soon, which means a segment from an earlier incarnation of a connection might interfere with a later incarnation of the connection.", "section_idx": 1, "section_name": "Example", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The Simple Mail Transfer Protocol (SMTP) is the key Internet standard for email transmission. It includes handshaking to negotiate authentication, encryption and maximum message size. ", "section_idx": 1, "section_name": "Example", "target_page_ids": [ 27675, 27675 ], "anchor_spans": [ [ 4, 33 ], [ 97, 117 ] ] }, { "plaintext": "When a Transport Layer Security (SSL or TLS) connection starts, the record encapsulates a \"control\" protocol—the handshake messaging protocol (content type 22). This protocol is used to exchange all the information required by both sides for the exchange of the actual application data by TLS. It defines the messages formatting or containing this information and the order of their exchange. These may vary according to the demands of the client and server—i.e., there are several possible procedures to set up the connection. This initial exchange results in a successful TLS connection (both parties ready to transfer application data with TLS) or an alert message (as specified below).", "section_idx": 1, "section_name": "Example", "target_page_ids": [ 187813 ], "anchor_spans": [ [ 7, 31 ] ] }, { "plaintext": "The protocol is used to negotiate the secure attributes of a session. (RFC 5246, p.37)", "section_idx": 1, "section_name": "Example", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The WPA2 standard for wireless uses a four-way handshake defined in IEEE 802.11i-2004.", "section_idx": 1, "section_name": "Example", "target_page_ids": [ 422017, 783135 ], "anchor_spans": [ [ 4, 30 ], [ 68, 85 ] ] }, { "plaintext": "One classic example of handshaking is that of dial-up modems, which typically negotiate communication parameters for a brief period when a connection is first established, and there after use those parameters to provide optimal information transfer over the channel as a function of its quality and capacity. The \"squealing\" (which is actually a sound that changes in pitch 100 times every second) noises made by some modems with speaker output immediately after a connection is established are in fact the sounds of modems at both ends engaging in a handshaking procedure; once the procedure is completed, the speaker might be silenced, depending on the settings of operating system or the application controlling the modem.", "section_idx": 1, "section_name": "Example", "target_page_ids": [ 59546, 20647197 ], "anchor_spans": [ [ 46, 53 ], [ 54, 59 ] ] }, { "plaintext": "This frequently used term describes the use of RTS and CTS signals over a serial interconnection. It is, however, not quite correct; it's not a true form of handshaking, and is better described as flow control.", "section_idx": 1, "section_name": "Example", "target_page_ids": [ 26023 ], "anchor_spans": [ [ 198, 210 ] ] }, { "plaintext": "Datenflusssteuerung", "section_idx": 2, "section_name": "References", "target_page_ids": [], "anchor_spans": [] } ]

[ "Data_transmission", "Network_architecture", "Network_protocols" ]

[ "Handshake" ]

[ { "plaintext": "In information handling, the U.S. Federal Standard 1037C (Glossary of Telecommunication Terms) defines a hard copy as a permanent reproduction, or copy, in the form of a physical object, of any media suitable for direct use by a person (in particular paper), of displayed or transmitted data. Examples of hard copies include teleprinter pages, continuous printed tapes, computer printouts, and radio photo prints. On the other hand, physical objects such as magnetic tapes, floppy disks, or non-printed punched paper tapes are not defined as hard copies by 1037C.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 315578, 37310, 16861908, 18985040, 31247, 20505, 10891, 49761 ], "anchor_spans": [ [ 3, 23 ], [ 34, 56 ], [ 251, 256 ], [ 287, 291 ], [ 325, 336 ], [ 458, 471 ], [ 474, 486 ], [ 503, 522 ] ] }, { "plaintext": "A file that can be viewed without printing on a screen is sometimes called a soft copy. The U.S. Federal Standard 1037C defines \"soft copy\" as \"a nonpermanent display image, for example, a cathode ray tube display.\"", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 6014 ], "anchor_spans": [ [ 189, 213 ] ] }, { "plaintext": "The term \"hard copy\" predates the digital computer. In the book and newspaper printing process, \"hard copy\" refers to a manuscript or typewritten document that has been edited and proofread and is ready for typesetting or being read on-air in a radio or television broadcast. The old meaning of hard copy was mostly discarded after the information revolution.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 169180, 2100075 ], "anchor_spans": [ [ 207, 218 ], [ 336, 358 ] ] }, { "plaintext": "One often-overlooked use for printers is in the field of IT security. Copies of various system and server activity logs are typically stored on the local filesystem, where a remote attacker – having achieved their primary goals – can then alter or delete the contents of the logs in an attempt to \"cover their tracks\" or otherwise thwart the efforts of system administrators and security experts. However, if the log entries are simultaneously given to a printer, line-by-line, a local hard-copy record of system activity is created – which cannot be remotely altered or otherwise manipulated. Dot matrix printers are ideal for this task, as they can sequentially print each log entry, one at a time, as they are added to the log. The usual dot-matrix printer support for continuous stationery also prevents incriminating pages from being surreptitiously removed or altered without evidence of tampering.", "section_idx": 1, "section_name": "Use in computer security", "target_page_ids": [ 7398, 1010280, 1040783 ], "anchor_spans": [ [ 57, 68 ], [ 154, 164 ], [ 594, 613 ] ] }, { "plaintext": "The hacker's Jargon File defines a dead-tree version to be a paper version of an online document, where \"dead trees\" refer to paper.", "section_idx": 2, "section_name": "\"Dead-tree\" dysphemism", "target_page_ids": [ 25523630 ], "anchor_spans": [ [ 13, 24 ] ] }, { "plaintext": "A saying from the Jargon File is that \"You can't grep dead trees\", which comes from the Unix command , which searches the contents of text files. This means that there is an advantage to keeping documents in digital form, rather than on paper, so that they can be more easily searched for specific contents. A similarly entry in the Jargon File is \"tree-killer\", which may refer either to a printer or a person who wastes paper.", "section_idx": 2, "section_name": "\"Dead-tree\" dysphemism", "target_page_ids": [ 46642, 21347364 ], "anchor_spans": [ [ 49, 53 ], [ 88, 92 ] ] }, { "plaintext": "Dead-tree edition refers to a printed paper version of a written work, as opposed to digital alternatives such as a web page.", "section_idx": 2, "section_name": "\"Dead-tree\" dysphemism", "target_page_ids": [ 16861908, 21076839 ], "anchor_spans": [ [ 38, 43 ], [ 116, 124 ] ] }, { "plaintext": "Hardcopy", "section_idx": 4, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Information_technology" ]

[ "physical copy", "hardcopies", "reprographic copies", "printout", "printed copy", "paper copy", "physical edition", "dead-tree edition", "dead tree", "dead-tree version", "physical version" ]

[ { "plaintext": "Hard sectoring in a magnetic or optical data storage device is a form of sectoring which uses a physical mark or hole in the recording medium to reference sector locations.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 896356, 41458, 28174, 8168684 ], "anchor_spans": [ [ 20, 28 ], [ 32, 39 ], [ 40, 59 ], [ 73, 79 ] ] }, { "plaintext": "In older 8- and 5-inch floppy disks, hard sectoring was implemented by punching sector holes in the disk to mark the start", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 10891 ], "anchor_spans": [ [ 23, 34 ] ] }, { "plaintext": "of each sector. These were equally spaced holes, at a common radius. This was in addition to the index hole, situated between two sector holes, to mark the start of the entire track of sectors. When the index or sector hole was recognized by an optical sensor, a sector signal was generated. Timing electronics or software would use the faster timing of the index hole between sector holes, to generate an index signal. Data read and write is faster in this technique than soft sectoring as no operations are to be performed regarding the starting and ending points of tracks.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 235757 ], "anchor_spans": [ [ 245, 259 ] ] }, { "plaintext": "32 sector 8-inch floppy disks", "section_idx": 1, "section_name": "Storage formats using hard sectoring", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "10 sector and 16 sector 5-inch floppy disks", "section_idx": 1, "section_name": "Storage formats using hard sectoring", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Numerous magneto-optical formats", "section_idx": 1, "section_name": "Storage formats using hard sectoring", "target_page_ids": [ 385880 ], "anchor_spans": [ [ 9, 24 ] ] }, { "plaintext": "DVD-RAM", "section_idx": 1, "section_name": "Storage formats using hard sectoring", "target_page_ids": [ 454545 ], "anchor_spans": [ [ 0, 7 ] ] } ]

[ "Rotating_disc_computer_storage_media" ]

[]

[ { "plaintext": "A harmonic is a wave with a frequency that is a positive integer multiple of the fundamental frequency, the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the 1st harmonic, the other harmonics are known as higher harmonics. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a harmonic series.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33516, 10779, 14563, 11490, 10779, 76848, 324749, 76848, 14439 ], "anchor_spans": [ [ 16, 20 ], [ 28, 37 ], [ 57, 64 ], [ 81, 102 ], [ 108, 117 ], [ 134, 149 ], [ 161, 176 ], [ 303, 311 ], [ 428, 443 ] ] }, { "plaintext": "The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100Hz (2nd harmonic), 150Hz (3rd harmonic), 200Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50Hz.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 1198, 14121, 42986 ], "anchor_spans": [ [ 71, 80 ], [ 196, 198 ], [ 209, 211 ] ] }, { "plaintext": "In music, harmonics are used on string instruments and wind instruments as a way of producing sound on the instrument, particularly to play higher notes and, with strings, obtain notes that have a unique sound quality or \"tone colour\". On strings, bowed harmonics have a \"glassy\", pure tone. On stringed instruments, harmonics are played by touching (but not fully pressing down the string) at an exact point on the string while sounding the string (plucking, bowing, etc.); this allows the harmonic to sound, a pitch which is always higher than the fundamental frequency of the string.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Harmonics may also be called \"overtones\", \"partials\" or \"upper partials\". The difference between \"harmonic\" and \"overtone\" is that the term \"harmonic\" includes all of the notes in a series, including the fundamental frequency (e.g., the open string of a guitar). The term \"overtone\" only includes the pitches above the fundamental. In some music contexts, the terms \"harmonic\", \"overtone\" and \"partial\" are used fairly interchangeably.", "section_idx": 1, "section_name": "Terminology", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Most acoustic instruments emit complex tones containing many individual partials (component simple tones or sinusoidal waves), but the untrained human ear typically does not perceive those partials as separate phenomena. Rather, a musical note is perceived as one sound, the quality or timbre of that sound being a result of the relative strengths of the individual partials. Many acoustic oscillators, such as the human voice or a bowed violin string, produce complex tones that are more or less periodic, and thus are composed of partials that are near matches to integer multiples of the fundamental frequency and therefore resemble the ideal harmonics and are called \"harmonic partials\" or simply \"harmonics\" for convenience (although it's not strictly accurate to call a partial a harmonic, the first being real and the second being ideal).", "section_idx": 2, "section_name": "Characteristics", "target_page_ids": [ 77892, 22522, 38481, 220213, 32427, 76848 ], "anchor_spans": [ [ 286, 292 ], [ 390, 400 ], [ 415, 426 ], [ 432, 437 ], [ 438, 444 ], [ 497, 505 ] ] }, { "plaintext": "Oscillators that produce harmonic partials behave somewhat like one-dimensional resonators, and are often long and thin, such as a guitar string or a column of air open at both ends (as with the modern orchestral transverse flute). Wind instruments whose air column is open at only one end, such as trumpets and clarinets, also produce partials resembling harmonics. However they only produce partials matching the odd harmonics, at least in theory. The reality of acoustic instruments is such that none of them behaves as perfectly as the somewhat simplified theoretical models would predict.", "section_idx": 2, "section_name": "Characteristics", "target_page_ids": [ 521510, 389453, 30353, 6433 ], "anchor_spans": [ [ 80, 89 ], [ 213, 229 ], [ 299, 306 ], [ 312, 320 ] ] }, { "plaintext": "Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic partials. Some acoustic instruments emit a mix of harmonic and inharmonic partials but still produce an effect on the ear of having a definite fundamental pitch, such as pianos, strings plucked pizzicato, vibraphones, marimbas, and certain pure-sounding bells or chimes. Antique singing bowls are known for producing multiple harmonic partials or multiphonics.", "section_idx": 2, "section_name": "Characteristics", "target_page_ids": [ 292196, 23034, 50190, 1695056, 1445866 ], "anchor_spans": [ [ 91, 110 ], [ 272, 277 ], [ 296, 305 ], [ 381, 393 ], [ 449, 461 ] ] }, { "plaintext": " Other oscillators, such as cymbals, drum heads, and other percussion instruments, naturally produce an abundance of inharmonic partials and do not imply any particular pitch, and therefore cannot be used melodically or harmonically in the same way other instruments can.", "section_idx": 2, "section_name": "Characteristics", "target_page_ids": [ 5671 ], "anchor_spans": [ [ 28, 35 ] ] }, { "plaintext": "Dynamic tonality, building on the work of William Sethares, introduces the notion of pseudo-harmonic partials, in which the frequency of each partial is aligned to match the pitch of a corresponding note in a pseudo-Just tuning, thereby maximizing the consonance of that pseudo-harmonic timbre with notes of that pseudo-just tuning.", "section_idx": 2, "section_name": "Characteristics", "target_page_ids": [ 17014020, 24416039, 1664363 ], "anchor_spans": [ [ 0, 16 ], [ 42, 58 ], [ 252, 262 ] ] }, { "plaintext": "An overtone is any partial higher than the lowest partial in a compound tone. The relative strengths and frequency relationships of the component partials determine the timbre of an instrument. The similarity between the terms overtone and partial sometimes leads to their being loosely used interchangeably in a musical context, but they are counted differently, leading to some possible confusion. In the special case of instrumental timbres whose component partials closely match a harmonic series (such as with most strings and winds) rather than being inharmonic partials (such as with most pitched percussion instruments), it is also convenient to call the component partials \"harmonics\" but not strictly correct (because harmonics are numbered the same even when missing, while partials and overtones are only counted when present). This chart demonstrates how the three types of names (partial, overtone, and harmonic) are counted (assuming that the harmonics are present):", "section_idx": 3, "section_name": "Partials, overtones, and harmonics", "target_page_ids": [ 41480, 18839 ], "anchor_spans": [ [ 3, 11 ], [ 313, 318 ] ] }, { "plaintext": "In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g., recorder) this has the effect of making the note go up in pitch by an octave, but in more complex cases many other pitch variations are obtained. In some cases it also changes the timbre of the note. This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. The extended technique of playing multiphonics also produces harmonics. On string instruments it is possible to produce very pure sounding notes, called harmonics or flageolets by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a unison the tuning of strings that are not tuned to the unison. For example, lightly fingering the node found halfway down the highest string of a cello produces the same pitch as lightly fingering the node of the way down the second highest string. For the human voice see Overtone singing, which uses harmonics.", "section_idx": 3, "section_name": "Partials, overtones, and harmonics", "target_page_ids": [ 27406894, 26244, 37726, 77892, 23442958, 370779, 410014, 1445866, 50076, 359293, 6558, 63981 ], "anchor_spans": [ [ 8, 27 ], [ 140, 148 ], [ 210, 216 ], [ 320, 326 ], [ 403, 419 ], [ 440, 451 ], [ 457, 475 ], [ 487, 498 ], [ 528, 546 ], [ 746, 752 ], [ 892, 897 ], [ 1020, 1036 ] ] }, { "plaintext": "While it is true that electronically produced periodic tones (e.g. square waves or other non-sinusoidal waves) have \"harmonics\" that are whole number multiples of the fundamental frequency, practical instruments do not all have this characteristic. For example, higher \"harmonics\"' of piano notes are not true harmonics but are \"overtones\" and can be very sharp, i.e. a higher frequency than given by a pure harmonic series. This is especially true of instruments other than stringed or brass/woodwind ones, e.g., xylophone, drums, bells etc., where not all the overtones have a simple whole number ratio with the fundamental frequency. The fundamental frequency is the reciprocal of the period of the periodic phenomenon.", "section_idx": 3, "section_name": "Partials, overtones, and harmonics", "target_page_ids": [ 14439, 11490, 229940, 10779 ], "anchor_spans": [ [ 408, 423 ], [ 641, 662 ], [ 670, 680 ], [ 688, 694 ] ] }, { "plaintext": "The following table displays the stop points on a stringed instrument at which gentle touching of a string will force it into a harmonic mode when vibrated. String harmonics (flageolet tones) are described as having a \"flutelike, silvery quality\" that can be highly effective as a special color or tone color (timbre) when used and heard in orchestration. It is unusual to encounter natural harmonics higher than the fifth partial on any stringed instrument except the double bass, on account of its much longer strings.", "section_idx": 4, "section_name": "On stringed instruments", "target_page_ids": [ 77892, 47398 ], "anchor_spans": [ [ 310, 316 ], [ 341, 354 ] ] }, { "plaintext": "Occasionally a score will call for an artificial harmonic, produced by playing an overtone on an already stopped string. As a performance technique, it is accomplished by using two fingers on the fingerboard, the first to shorten the string to the desired fundamental, with the second touching the node corresponding to the appropriate harmonic.", "section_idx": 4, "section_name": "On stringed instruments", "target_page_ids": [ 8900795 ], "anchor_spans": [ [ 38, 57 ] ] }, { "plaintext": "Harmonics may be either used in or considered as the basis of just intonation systems. Composer Arnold Dreyblatt is able to bring out different harmonics on the single string of his modified double bass by slightly altering his unique bowing technique halfway between hitting and bowing the strings. Composer Lawrence Ball uses harmonics to generate music electronically.", "section_idx": 5, "section_name": "Other information", "target_page_ids": [ 16493, 387791, 8816, 220213, 12242584 ], "anchor_spans": [ [ 62, 77 ], [ 96, 112 ], [ 191, 202 ], [ 235, 241 ], [ 309, 322 ] ] }, { "plaintext": " Aristoxenus", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 98921 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Electronic tuner", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 4385464 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Formant", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 11024 ], "anchor_spans": [ [ 1, 8 ] ] }, { "plaintext": " Fourier series", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 59038 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Guitar harmonic", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 8900795 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Harmonic analysis", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 14147 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Harmonics (electrical power)", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 19196354 ], "anchor_spans": [ [ 1, 29 ] ] }, { "plaintext": " Harmonic oscillator", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 13899 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": " Harmonic series (music)", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 14439 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Harmony", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 40258 ], "anchor_spans": [ [ 1, 8 ] ] }, { "plaintext": " Pure tone", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 826809 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " Pythagorean tuning", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 42900 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Scale of harmonics", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 20947328 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Spherical harmonics", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 203056 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": " Stretched octave", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 321874 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Subharmonic", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 6816305 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Xenharmonic music", "section_idx": 6, "section_name": "See also", "target_page_ids": [ 321838 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " The Feynman Lectures on Physics: Harmonics", "section_idx": 8, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Harmonics, partials and overtones from fundamental frequency", "section_idx": 8, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Harmonics", "section_idx": 8, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Hear and see harmonics on a Piano", "section_idx": 8, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Acoustics", "Guitar_performance_techniques", "Telecommunications", "String_instruments", "Sound" ]

[ "overtone", "partial", "upper partial", "harmonic component" ]

[ { "plaintext": "In the Integrated Services Digital Network (ISDN), a high-speed communication channel comprising multiple aggregated low-speed channels to accommodate bandwidth-intensive applications such as file transfer, videoconferencing, and high-quality audio. An H channel is formed of multiple bearer B channels bonded together in a primary rate access (PRA) or primary rate interface (PRI) frame in support of applications with bandwidth requirements that exceed the B channel rate of 64 kbit/s. The channels, once bonded, remain so end-to-end, from transmitter to receiver, through the ISDN network. The feature is known variously as multirate ISDN, Nx64, channel aggregation, and bonding.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 15231, 156700, 3967, 7018709, 2304367, 521752, 41578, 61164, 1952952 ], "anchor_spans": [ [ 7, 42 ], [ 64, 85 ], [ 151, 160 ], [ 192, 205 ], [ 207, 224 ], [ 292, 301 ], [ 353, 375 ], [ 542, 553 ], [ 674, 681 ] ] }, { "plaintext": "H channels are implemented as:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " H0 = 384 kbit/s(6 B channels)", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " H10 = 1472 kbit/s(23 B channels)", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " H11 = 1536 kbit/s(24 B channels)", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " H12 = 1920 kbit/s(30 B channels) – International (E-carrier) only.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 46728 ], "anchor_spans": [ [ 51, 60 ] ] }, { "plaintext": " D channel", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 521815 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " B channel", "section_idx": 1, "section_name": "See also", "target_page_ids": [ 521752 ], "anchor_spans": [ [ 1, 10 ] ] } ]

[ "Integrated_Services_Digital_Network" ]

[]

[ { "plaintext": "A heterodyne is a signal frequency that is created by combining or mixing two other frequencies using a signal processing technique called heterodyning, which was invented by Canadian inventor-engineer Reginald Fessenden. Heterodyning is used to shift signals from one frequency range into another, and is also involved in the processes of modulation and demodulation. The two input frequencies are combined in a nonlinear signal-processing device such as a vacuum tube, transistor, or diode, usually called a mixer.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 275871, 10779, 29324, 96883, 5167862, 20637, 66926, 6769882, 32496, 30011, 8254, 482952 ], "anchor_spans": [ [ 18, 24 ], [ 25, 34 ], [ 104, 121 ], [ 202, 220 ], [ 269, 284 ], [ 340, 350 ], [ 355, 367 ], [ 413, 422 ], [ 458, 469 ], [ 471, 481 ], [ 486, 491 ], [ 510, 515 ] ] }, { "plaintext": "In the most common application, two signals at frequencies and are mixed, creating two new signals, one at the sum of the two frequencies , and the other at the difference between the two frequencies . The new signal frequencies are called heterodynes. Typically, only one of the heterodynes is required and the other signal is filtered out of the output of the mixer. Heterodyne frequencies are related to the phenomenon of \"beats\" in acoustics.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 23434533, 2101485 ], "anchor_spans": [ [ 331, 339 ], [ 429, 433 ] ] }, { "plaintext": "A major application of the heterodyne process is in the superheterodyne radio receiver circuit, which is used in virtually all modern radio receivers.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 29341 ], "anchor_spans": [ [ 56, 86 ] ] }, { "plaintext": "In 1901, Reginald Fessenden demonstrated a direct-conversion heterodyne receiver or beat receiver as a method of making continuous wave radiotelegraphy signals audible. Fessenden's receiver did not see much application because of its local oscillator's stability problem. A stable yet inexpensive local oscillator was not available until Lee de Forest invented the triode vacuum tube oscillator. In a 1905 patent, Fessenden stated that the frequency stability of his local oscillator was one part per thousand.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 96883, 2986919, 291706, 33131, 256764, 31036 ], "anchor_spans": [ [ 9, 27 ], [ 43, 80 ], [ 120, 135 ], [ 136, 151 ], [ 340, 353 ], [ 367, 385 ] ] }, { "plaintext": "In radio telegraphy, the characters of text messages are translated into the short duration dots and long duration dashes of Morse code that are broadcast as radio signals. Radio telegraphy was much like ordinary telegraphy. One of the problems was building high power transmitters with the technology of the day. Early transmitters were spark gap transmitters. A mechanical device would make sparks at a fixed but audible rate; the sparks would put energy into a resonant circuit that would then ring at the desired transmission frequency (which might be 100kHz). This ringing would quickly decay, so the output of the transmitter would be a succession of damped waves. When these damped waves were received by a simple detector, the operator would hear an audible buzzing sound that could be transcribed back into alpha-numeric characters.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 18935, 33131, 30010, 1105907, 1744868 ], "anchor_spans": [ [ 125, 135 ], [ 173, 189 ], [ 213, 223 ], [ 338, 359 ], [ 657, 668 ] ] }, { "plaintext": "With the development of the arc converter radio transmitter in 1904, continuous wave (CW) modulation began to be used for radiotelegraphy. CW Morse code signals are not amplitude modulated, but rather consist of bursts of sinusoidal carrier frequency. When CW signals are received by an AM receiver, the operator does not hear a sound. The direct-conversion (heterodyne) detector was invented to make continuous wave radio-frequency signals audible.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 4196082, 291706 ], "anchor_spans": [ [ 28, 41 ], [ 69, 84 ] ] }, { "plaintext": "The \"heterodyne\" or \"beat\" receiver has a local oscillator that produces a radio signal adjusted to be close in frequency to the incoming signal being received. When the two signals are mixed, a \"beat\" frequency equal to the difference between the two frequencies is created. Adjusting the local oscillator frequency correctly puts the beat frequency in the audio range, where it can be heard as a tone in the receiver's earphones whenever the transmitter signal is present. Thus the Morse code \"dots\" and \"dashes\" are audible as beeping sounds. This technique is still used in radio telegraphy, the local oscillator now being called the beat frequency oscillator or BFO. Fessenden coined the word heterodyne from the Greek roots hetero- \"different\", and dyn- \"power\" (cf. δύναμις or dunamis).", "section_idx": 1, "section_name": "History", "target_page_ids": [ 2124436, 12812363, 191884, 509950 ], "anchor_spans": [ [ 42, 58 ], [ 360, 365 ], [ 423, 431 ], [ 640, 665 ] ] }, { "plaintext": "An important and widely used application of the heterodyne technique is in the superheterodyne receiver (superhet), which was invented by U.S. engineer Edwin Howard Armstrong in 1918. In the typical superhet, the incoming radio frequency signal from the antenna is mixed (heterodyned) with a signal from a local oscillator (LO) to produce a lower fixed frequency signal called the intermediate frequency (IF) signal. The IF signal is amplified and filtered and then applied to a detector that extracts the audio signal; the audio is ultimately sent to the receiver's loudspeaker.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 29341, 10315, 42852, 83139, 4529151 ], "anchor_spans": [ [ 79, 103 ], [ 152, 174 ], [ 222, 237 ], [ 381, 403 ], [ 479, 487 ] ] }, { "plaintext": "The superheterodyne receiver has several advantages over previous receiver designs. One advantage is easier tuning; only the RF filter and the LO are tuned by the operator; the fixed-frequency IF is tuned (\"aligned\") at the factory and is not adjusted. In older designs such as the tuned radio frequency receiver (TRF), all of the receiver stages had to be simultaneously tuned. In addition, since the IF filters are fixed-tuned, the receiver's selectivity is the same across the receiver's entire frequency band. Another advantage is that the IF signal can be at a much lower frequency than the incoming radio signal, and that allows each stage of the IF amplifier to provide more gain. To first order, an amplifying device has a fixed gain-bandwidth product. If the device has a gain-bandwidth product of 60MHz, then it can provide a voltage gain of 3 at an RF of 20MHz or a voltage gain of 30 at an IF of 2MHz. At a lower IF, it would take fewer gain devices to achieve the same gain. The regenerative radio receiver obtained more gain out of one gain device by using positive feedback, but it required careful adjustment by the operator; that adjustment also changed the selectivity of the regenerative receiver. The superheterodyne provides a large, stable gain and constant selectivity without troublesome adjustment.", "section_idx": 1, "section_name": "History", "target_page_ids": [ 482137, 3255700, 343276 ], "anchor_spans": [ [ 282, 312 ], [ 737, 759 ], [ 992, 1019 ] ] }, { "plaintext": "The superior superheterodyne system replaced the earlier TRF and regenerative receiver designs, and since the 1930s most commercial radio receivers have been superheterodynes.", "section_idx": 1, "section_name": "History", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Heterodyning, also called frequency conversion, is used very widely in communications engineering to generate new frequencies and move information from one frequency channel to another. Besides its use in the superheterodyne circuit found in almost all radio and television receivers, it is used in radio transmitters, modems, satellite communications and set-top boxes, radar, radio telescopes, telemetry systems, cell phones, cable television converter boxes and headends, microwave relays, metal detectors, atomic clocks, and military electronic countermeasure (jamming) systems.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 8774050, 61164, 20647197, 27683, 25676, 46656, 46256, 353080, 5540651, 165015, 25453985, 879940 ], "anchor_spans": [ [ 71, 97 ], [ 299, 316 ], [ 319, 324 ], [ 327, 336 ], [ 371, 376 ], [ 378, 393 ], [ 396, 405 ], [ 465, 473 ], [ 475, 490 ], [ 493, 507 ], [ 510, 522 ], [ 538, 563 ] ] }, { "plaintext": "In large scale telecommunication networks such as telephone network trunks, microwave relay networks, cable television systems, and communication satellite links, large bandwidth capacity links are shared by many individual communication channels by using heterodyning to move the frequency of the individual signals up to different frequencies, which share the channel. This is called frequency division multiplexing (FDM).", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 46545, 1966111, 5540651, 45207, 3967, 86376 ], "anchor_spans": [ [ 15, 40 ], [ 50, 67 ], [ 76, 91 ], [ 132, 155 ], [ 169, 178 ], [ 386, 417 ] ] }, { "plaintext": "For example, a coaxial cable used by a cable television system can carry 500 television channels at the same time because each one is given a different frequency, so they do not interfere with one another. At the cable source or headend, electronic upconverters convert each incoming television channel to a new, higher frequency. They do this by mixing the television signal frequency, fCH with a local oscillator at a much higher frequency , creating a heterodyne at the sum , which is added to the cable. At the consumer's home, the cable set top box has a downconverter that mixes the incoming signal at frequency with the same local oscillator frequency creating the difference heterodyne frequency, converting the television channel back to its original frequency: . Each channel is moved to a different higher frequency. The original lower basic frequency of the signal is called the baseband, while the higher channel it is moved to is called the passband.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 46380, 353080, 2124436, 29580, 40773, 41488 ], "anchor_spans": [ [ 15, 28 ], [ 229, 236 ], [ 399, 415 ], [ 543, 554 ], [ 896, 904 ], [ 960, 968 ] ] }, { "plaintext": "Many analog videotape systems rely on a downconverted color subcarrier to record color information in their limited bandwidth. These systems are referred to as \"heterodyne systems\" or \"color-under systems\". For instance, for NTSC video systems, the VHS (and S-VHS) recording system converts the color subcarrier from the NTSC standard 3.58MHz to ~629kHz. PAL VHS color subcarrier is similarly downconverted (but from 4.43MHz). The now-obsolete 3/4\" U-matic systems use a heterodyned ~688kHz subcarrier for NTSC recordings (as does Sony's Betamax, which is at its basis a 1/2″ consumer version of U-matic), while PAL U-matic decks came in two mutually incompatible varieties, with different subcarrier frequencies, known as Hi-Band and Low-Band. Other videotape formats with heterodyne color systems include Video-8 and Hi8.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 147952, 21689, 52124, 159598, 24438, 1286331, 26989, 188578, 948376, 948376 ], "anchor_spans": [ [ 12, 21 ], [ 225, 229 ], [ 249, 252 ], [ 258, 263 ], [ 355, 358 ], [ 449, 456 ], [ 531, 535 ], [ 538, 545 ], [ 807, 814 ], [ 819, 822 ] ] }, { "plaintext": "The heterodyne system in these cases is used to convert quadrature phase-encoded and amplitude modulated sine waves from the broadcast frequencies to frequencies recordable in less than 1MHz bandwidth. On playback, the recorded color information is heterodyned back to the standard subcarrier frequencies for display on televisions and for interchange with other standard video equipment.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Some U-matic (3/4″) decks feature 7-pin mini-DIN connectors to allow dubbing of tapes without conversion, as do some industrial VHS, S-VHS, and Hi8 recorders.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 330916 ], "anchor_spans": [ [ 45, 58 ] ] }, { "plaintext": "The theremin, an electronic musical instrument, traditionally uses the heterodyne principle to produce a variable audio frequency in response to the movement of the musician's hands in the vicinity of one or more antennae, which act as capacitor plates. The output of a fixed radio frequency oscillator is mixed with that of an oscillator whose frequency is affected by the variable capacitance between the antenna and the musician's hand as it is moved near the pitch control antenna. The difference between the two oscillator frequencies produces a tone in the audio range.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 30722, 10006, 344142, 2549117 ], "anchor_spans": [ [ 4, 12 ], [ 17, 46 ], [ 114, 129 ], [ 374, 394 ] ] }, { "plaintext": "The ring modulator is a type of frequency mixer incorporated into some synthesizers or used as a stand-alone audio effect.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 275872, 482952 ], "anchor_spans": [ [ 4, 18 ], [ 32, 47 ] ] }, { "plaintext": "Optical heterodyne detection (an area of active research) is an extension of the heterodyning technique to higher (visible) frequencies. Guerra (1995) first published the results of what he called a \"form of optical heterodyning\" in which light patterned by a 50 nm pitch grating illuminated a second grating of pitch 50 nm, with the gratings rotated with respect to each other by the angular amount needed to achieve magnification. Although the illuminating wavelength was 650 nm, the 50 nm grating was easily resolved. This showed a nearly 5-fold improvement over the Abbe resolution limit of 232 nm that should have been the smallest obtained for the numerical aperture and wavelength used. This super-resolution microscopic imaging through optical heterodyning later came to be know by many as \"structured illumination microscopy\". ", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 18515482 ], "anchor_spans": [ [ 0, 28 ] ] }, { "plaintext": "In addition to super-resolution optical microscopy, optical heterodyning could greatly improve optical modulators, increasing the density of information carried by optical fibers. It is also being applied in the creation of more accurate atomic clocks based on directly measuring the frequency of a laser beam. See NIST subtopic 9.07.9-4.R for a description of research on one system to do this.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 4466344, 3372377, 25453985 ], "anchor_spans": [ [ 95, 112 ], [ 164, 177 ], [ 238, 250 ] ] }, { "plaintext": "Since optical frequencies are far beyond the manipulation capacity of any feasible electronic circuit, all visible frequency photon detectors are inherently energy detectors not oscillating electric field detectors. However, since energy detection is inherently \"square-law\" detection, it intrinsically mixes any optical frequencies present on the detector. Thus, sensitive detection of specific optical frequencies necessitates optical heterodyne detection, in which two different (close-by) wavelengths of light illuminate the detector so that the oscillating electrical output corresponds to the difference between their frequencies. This allows extremely narrow band detection (much narrower than any possible color filter can achieve) as well as precision measurements of phase and frequency of a light signal relative to a reference light source, as in a laser Doppler vibrometer.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 59657820, 19377279 ], "anchor_spans": [ [ 263, 273 ], [ 861, 885 ] ] }, { "plaintext": "This phase sensitive detection has been applied for Doppler measurements of wind speed, and imaging through dense media. The high sensitivity against background light is especially useful for lidar.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 41958 ], "anchor_spans": [ [ 192, 197 ] ] }, { "plaintext": "In optical Kerr effect (OKE) spectroscopy, optical heterodyning of the OKE signal and a small part of the probe signal produces a mixed signal consisting of probe, heterodyne OKE-probe and homodyne OKE signal. The probe and homodyne OKE signals can be filtered out, leaving the heterodyne frequency signal for detection.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 661039 ], "anchor_spans": [ [ 3, 22 ] ] }, { "plaintext": "Heterodyne detection is often used in interferometry but usually confined to single point detection rather than widefield interferometry, however, widefield heterodyne interferometry is possible using a special camera. Using this technique which a reference signal extracted from a single pixel it is possible to build a highly stable widefield heterodyne interferometer by removing the piston phase component", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 166689 ], "anchor_spans": [ [ 38, 52 ] ] }, { "plaintext": "caused by microphonics or vibrations of the optical components or object.", "section_idx": 2, "section_name": "Applications", "target_page_ids": [ 682186 ], "anchor_spans": [ [ 10, 22 ] ] }, { "plaintext": "Heterodyning is based on the trigonometric identity:", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [ 25804104 ], "anchor_spans": [ [ 29, 51 ] ] }, { "plaintext": "The product on the left hand side represents the multiplication (\"mixing\") of a sine wave with another sine wave. The right hand side shows that the resulting signal is the difference of two sinusoidal terms, one at the sum of the two original frequencies, and one at the difference, which can be considered to be separate signals.", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [ 324749, 324749 ], "anchor_spans": [ [ 80, 89 ], [ 191, 201 ] ] }, { "plaintext": "Using this trigonometric identity, the result of multiplying two sine wave signals and at different frequencies and can be calculated:", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The result is the sum of two sinusoidal signals, one at the sum and one at the difference of the original frequencies.", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The two signals are combined in a device called a mixer. As seen in the previous section, an ideal mixer would be a device that multiplies the two signals. Some widely used mixer circuits, such as the Gilbert cell, operate in this way, but they are limited to lower frequencies. However, any nonlinear electronic component also multiplies signals applied to it, producing heterodyne frequencies in its output—so a variety of nonlinear components serve as mixers. A nonlinear component is one in which the output current or voltage is a nonlinear function of its input. Most circuit elements in communications circuits are designed to be linear. This means they obey the superposition principle; if is the output of a linear element with an input of :", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [ 482952, 13246370, 6769882, 152111, 6769882, 1201321 ], "anchor_spans": [ [ 50, 55 ], [ 203, 215 ], [ 295, 304 ], [ 539, 557 ], [ 640, 646 ], [ 673, 696 ] ] }, { "plaintext": "So if two sine wave signals at frequencies and are applied to a linear device, the output is simply the sum of the outputs when the two signals are applied separately with no product terms. Thus, the function must be nonlinear to create mixer products. A perfect multiplier only produces mixer products at the sum and difference frequencies , but more general nonlinear functions produce higher order mixer products: for integers and . Some mixer designs, such as double-balanced mixers, suppress some high order undesired products, while other designs, such as harmonic mixers exploit high order differences.", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [ 5779959 ], "anchor_spans": [ [ 569, 583 ] ] }, { "plaintext": "Examples of nonlinear components that are used as mixers are vacuum tubes and transistors biased near cutoff (class C), and diodes. Ferromagnetic core inductors driven into saturation can also be used at lower frequencies. In nonlinear optics, crystals that have nonlinear characteristics are used to mix laser light beams to create optical heterodyne frequencies.", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [ 32496, 30011, 54005385, 8254, 1516916, 14896, 2159714, 21723, 17556, 18515482 ], "anchor_spans": [ [ 61, 72 ], [ 78, 88 ], [ 110, 117 ], [ 124, 129 ], [ 132, 150 ], [ 151, 159 ], [ 173, 183 ], [ 226, 242 ], [ 305, 310 ], [ 333, 363 ] ] }, { "plaintext": "To demonstrate mathematically how a nonlinear component can multiply signals and generate heterodyne frequencies, the nonlinear function can be expanded in a power series (MacLaurin series):", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [ 59958, 30448 ], "anchor_spans": [ [ 159, 171 ], [ 173, 189 ] ] }, { "plaintext": "To simplify the math, the higher order terms above are indicated by an ellipsis (\"...\") and only the first terms are shown. Applying the two sine waves at frequencies and to this device:", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "It can be seen that the second term above contains a product of the two sine waves. Simplifying with trigonometric identities:", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [ 25804104 ], "anchor_spans": [ [ 101, 125 ] ] }, { "plaintext": "So the output contains sinusoidal terms with frequencies at the sum and difference of the two original frequencies. It also contains terms at the original frequencies and at multiples of the original frequencies , , , , etc.; the latter are called harmonics, as well as more complicated terms at frequencies of , called intermodulation products. These unwanted frequencies, along with the unwanted heterodyne frequency, must be filtered out of the mixer output by an electronic filter to leave the desired frequency.", "section_idx": 3, "section_name": "Mathematical principle", "target_page_ids": [ 41232, 590995, 1866533 ], "anchor_spans": [ [ 250, 259 ], [ 322, 345 ], [ 469, 486 ] ] }, { "plaintext": " Electroencephalography", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 21402632 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Homodyne", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 1489315 ], "anchor_spans": [ [ 1, 9 ] ] }, { "plaintext": " Transverter", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 3121088 ], "anchor_spans": [ [ 1, 12 ] ] }, { "plaintext": " Intermodulation – a problem with strong higher-order terms produced in some non-linear mixers", "section_idx": 4, "section_name": "See also", "target_page_ids": [ 590995 ], "anchor_spans": [ [ 1, 16 ] ] } ]

[ "Frequency_mixers", "Signal_processing" ]

[]

[ { "plaintext": "Heuristic routing is a system used to describe how deliveries are made when problems in a network topology arise. Heuristic is an adjective used in relation to methods of learning, discovery, or problem solving. Routing is the process of selecting paths to specific destinations. Heuristic routing is used for traffic in the telecommunications networks and transport networks of the world.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 41413, 63452, 25750, 46545, 1457428 ], "anchor_spans": [ [ 90, 106 ], [ 114, 123 ], [ 212, 219 ], [ 326, 352 ], [ 358, 375 ] ] }, { "plaintext": "Heuristic routing is achieved using specific algorithms to determine a better, although not always optimal, path to a destination. When an interruption in a network topology occurs, the software running on the networking electronics can calculate another route to the desired destination via an alternate available path.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 775 ], "anchor_spans": [ [ 45, 54 ] ] }, { "plaintext": "According to :", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "The heuristic approach to problem solving consists of applying human intelligence, experience, common sense and certain rules of thumb (or heuristics) to develop an acceptable, but not necessarily an optimum, solution to a problem. Of course, determining what constitutes an acceptable solution is part of the task of deciding which approach to use; but broadly defined, an acceptable solution is one that is both reasonably good (close to optimum) and derived within reasonable effort, time, and cost constraints. Often the effort (manpower, computer, and other resources) required, the time limits on when the solution is needed, and the cost to compile, process, and analyze all the data required for deterministic or other complicated procedures preclude their usefulness or favor the faster, simpler heuristic approach. Thus, the heuristic approach is generally used when deterministic techniques or are not available, economical, or practical.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Heuristic routing allows a measure of route optimization in telecommunications networks based on recent empirical knowledge of the state of the network. Data, such as time delay, may be extracted from incoming messages, during specified periods and over different routes, and used to determine the optimum routing for transmitting data back to the sources. ", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 30012, 10145584 ], "anchor_spans": [ [ 167, 171 ], [ 172, 177 ] ] }, { "plaintext": "The IP routing protocols in use today are based on one of two algorithms: distance vector or link state. Distance vector algorithms broadcast routing information to all neighboring routers. Link state routing protocols build a topographical map of the entire network based on updates from neighbor routers, and then use the Dijkstra algorithm to compute the shortest path to each destination. Metrics used are based on the number of hops, delay, throughput, traffic, and reliability.", "section_idx": 1, "section_name": "IP routing", "target_page_ids": [ 27385819, 45809 ], "anchor_spans": [ [ 4, 14 ], [ 324, 342 ] ] }, { "plaintext": "RIP uses number of hops, or gateways traversed, as its metric", "section_idx": 1, "section_name": "IP routing", "target_page_ids": [ 43389 ], "anchor_spans": [ [ 0, 3 ] ] }, { "plaintext": "IGRP uses bandwidth, delay, hop count, link reliability, load, and MTU", "section_idx": 1, "section_name": "IP routing", "target_page_ids": [ 14844, 20894 ], "anchor_spans": [ [ 0, 4 ], [ 67, 70 ] ] }, { "plaintext": "EIGRP uses the (DUAL) Diffusing Update Algorithm", "section_idx": 1, "section_name": "IP routing", "target_page_ids": [ 51544, 2085170 ], "anchor_spans": [ [ 0, 5 ], [ 22, 48 ] ] }, { "plaintext": "BGP uses the distance vector algorithm", "section_idx": 1, "section_name": "IP routing", "target_page_ids": [ 38893 ], "anchor_spans": [ [ 0, 3 ] ] }, { "plaintext": "OSPF uses the Dijkstra algorithm.", "section_idx": 1, "section_name": "IP routing", "target_page_ids": [ 43388, 45809 ], "anchor_spans": [ [ 0, 4 ], [ 14, 32 ] ] }, { "plaintext": "Heuristic (computer science)", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 14220429 ], "anchor_spans": [ [ 0, 28 ] ] }, { "plaintext": "Ford–Fulkerson algorithm", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 53777 ], "anchor_spans": [ [ 0, 24 ] ] }, { "plaintext": "Bellman–Ford algorithm", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 221244 ], "anchor_spans": [ [ 0, 22 ] ] }, { "plaintext": "Turn restriction routing", "section_idx": 2, "section_name": "See also", "target_page_ids": [ 52413716 ], "anchor_spans": [ [ 0, 24 ] ] } ]

[ "Heuristic_algorithms", "Routing" ]

[]

[ { "plaintext": "Hierarchical routing is a method of routing in networks that is based on hierarchical addressing.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 25750, 8168925 ], "anchor_spans": [ [ 37, 44 ], [ 87, 97 ] ] }, { "plaintext": "Most Transmission Control Protocol/Internet Protocol (TCP/IP) routing is based on a two-level hierarchical routing in which an IP address is divided into a network portion and a host portion. Gateways use only the network portion until an IP datagram reaches a gateway that can deliver it directly. Additional levels of hierarchical routing are introduced by the addition of subnetworks.", "section_idx": 1, "section_name": "Background", "target_page_ids": [ 30538, 15323, 15476, 8168925, 4122592, 42116, 40994, 1338556 ], "anchor_spans": [ [ 5, 34 ], [ 35, 52 ], [ 54, 60 ], [ 130, 137 ], [ 156, 163 ], [ 178, 182 ], [ 242, 250 ], [ 261, 268 ] ] }, { "plaintext": "Hierarchical routing is the procedure of arranging routers in a hierarchical manner. A good example would be to consider a corporate intranet. Most corporate intranets consist of a high speed backbone network. Connected to this backbone are routers which are in turn connected to a particular workgroup. These workgroups occupy a unique LAN. The reason this is a good arrangement is because even though there might be dozens of different workgroups, the span (maximum hop count to get from one host to any other host on the network) is 2. Even if the workgroups divided their LAN network into smaller partitions, the span could only increase to 4 in this particular example.", "section_idx": 2, "section_name": "Description", "target_page_ids": [ 25748, 37481, 2853516, 17739, 22824905 ], "anchor_spans": [ [ 51, 57 ], [ 133, 141 ], [ 192, 208 ], [ 337, 340 ], [ 468, 477 ] ] }, { "plaintext": "Considering alternative solutions with every router connected to every other router, or if every router was connected to 2 routers, shows the convenience of hierarchical routing. It decreases the complexity of network topology, increases routing efficiency, and causes much less congestion because of fewer routing advertisements. With hierarchical routing, only core routers connected to the backbone are aware of all routes. Routers that lie within a LAN only know about routes in the LAN. Unrecognized destinations are passed to the default route.", "section_idx": 2, "section_name": "Description", "target_page_ids": [ 41413, 430522 ], "anchor_spans": [ [ 210, 226 ], [ 279, 289 ] ] }, { "plaintext": "http://www.isi.edu/nsnam/ns/doc-stable/node310.html", "section_idx": 4, "section_name": "External links", "target_page_ids": [], "anchor_spans": [] } ]

[ "Routing" ]

[]

[ { "plaintext": "High-performance equipment describes telecommunications equipment that", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 33094374 ], "anchor_spans": [ [ 37, 55 ] ] }, { "plaintext": "(a) has the performance characteristics required for use in trunks or links,", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "(b) is designed primarily for use in global and tactical systems, and", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "(c) sufficiently withstands electromagnetic interference when operating in a variety of network or point-to-point circuits.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 1072324, 46545 ], "anchor_spans": [ [ 28, 56 ], [ 88, 95 ] ] }, { "plaintext": "Note: Requirements for global and tactical high-performance equipment may differ.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] } ]

[ "Telecommunications_equipment" ]

[]

[ { "plaintext": "A hop is a type of jump.", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 43609 ], "anchor_spans": [ [ 19, 23 ] ] }, { "plaintext": "Hop or hops may also refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Hop (film), a 2011 film", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 27888241 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Hop! Channel, an Israeli TV channel", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 50789061 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " House of Payne, or HOP, an American sitcom", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 5104049 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Lindy Hop, a swing dance of the 1920s and 1930s", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 39809074 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " Sock hop, an informal gathering which includes dancing", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 570124 ], "anchor_spans": [ [ 1, 9 ] ] }, { "plaintext": " Hop Harrigan, a character in American comic books, radio serials and film serials from 1939 into the 1940s", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 3377233 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Hop, a character from Pokémon Sword and Shield", "section_idx": 1, "section_name": "Arts and entertainment", "target_page_ids": [ 60088996 ], "anchor_spans": [ [ 23, 47 ] ] }, { "plaintext": " Hop Bartlett, American baseball pitcher in the Negro leagues in 1924 and 1925", "section_idx": 2, "section_name": "People", "target_page_ids": [ 66182051 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Hop Wilson (1921–1975), American Texas blues steel guitar player", "section_idx": 2, "section_name": "People", "target_page_ids": [ 25301881 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Hop River, Connecticut, United States", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 12164129 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " Hop Creek, South Dakota, United States", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 49412559 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " Hóp (Iceland), a lake", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 693220 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Hóp, a Viking settlement in Vinland", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 32545 ], "anchor_spans": [ [ 29, 36 ] ] }, { "plaintext": " Humulus lupulus, the hop plant", "section_idx": 4, "section_name": "Plants", "target_page_ids": [ 1912301 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Hops, its flower, used to prepare beer and other food", "section_idx": 4, "section_name": "Plants", "target_page_ids": [ 14352 ], "anchor_spans": [ [ 1, 5 ] ] }, { "plaintext": " HOP (gene), encoding the homeodomain-only protein", "section_idx": 5, "section_name": "Science and medicine", "target_page_ids": [ 14798104 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Hop (protein), the Hsp70-Hsp90 organizing protein", "section_idx": 5, "section_name": "Science and medicine", "target_page_ids": [ 1406446 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Hubble Origins Probe, or HOP, a proposed orbital telescope", "section_idx": 5, "section_name": "Science and medicine", "target_page_ids": [ 1471966 ], "anchor_spans": [ [ 1, 21 ] ] }, { "plaintext": " Hop (networking), a portion of a route ", "section_idx": 6, "section_name": "Technology", "target_page_ids": [ 22824905 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Hop (software), a web broker and programming language", "section_idx": 6, "section_name": "Technology", "target_page_ids": [ 13433106 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Hop (telecommunications)", "section_idx": 6, "section_name": "Technology", "target_page_ids": [ 55184 ], "anchor_spans": [ [ 1, 25 ] ] }, { "plaintext": " Hindsight optimization, or Hop, an artificial intelligence technique", "section_idx": 6, "section_name": "Technology", "target_page_ids": [ 36831006 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " High Octet Preset, or HOP, a C1 control character", "section_idx": 6, "section_name": "Technology", "target_page_ids": [ 2371820 ], "anchor_spans": [ [ 30, 50 ] ] }, { "plaintext": " Spike (application), an email app formerly known as Hop", "section_idx": 6, "section_name": "Technology", "target_page_ids": [ 62775183 ], "anchor_spans": [ [ 1, 20 ] ] }, { "plaintext": " Air France Hop, a French airline", "section_idx": 7, "section_name": "Transport", "target_page_ids": [ 38971555 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " HOP card, a smart card used on public transit in Auckland, New Zealand", "section_idx": 7, "section_name": "Transport", "target_page_ids": [ 32026892 ], "anchor_spans": [ [ 1, 9 ] ] }, { "plaintext": " Heritage Operations Processing System, a tool for management of historic railways", "section_idx": 7, "section_name": "Transport", "target_page_ids": [ 41902674 ], "anchor_spans": [ [ 1, 38 ] ] }, { "plaintext": " Hope (Derbyshire) railway station, in England", "section_idx": 7, "section_name": "Transport", "target_page_ids": [ 1871466 ], "anchor_spans": [ [ 1, 34 ] ] }, { "plaintext": " Hope (Flintshire) railway station, in Wales ", "section_idx": 7, "section_name": "Transport", "target_page_ids": [ 4615846 ], "anchor_spans": [ [ 1, 34 ] ] }, { "plaintext": " \"The Hop\", the brand for public transport in Sydney and New South Wales", "section_idx": 7, "section_name": "Transport", "target_page_ids": [ 5283968 ], "anchor_spans": [ [ 26, 52 ] ] }, { "plaintext": " \"The Hop (streetcar)\", streetcar system in Milwaukee", "section_idx": 7, "section_name": "Transport", "target_page_ids": [ 45294932 ], "anchor_spans": [ [ 2, 21 ] ] }, { "plaintext": " Hop (unit), a small Korean unit of volume", "section_idx": 8, "section_name": "Other uses", "target_page_ids": [ 1645870 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Croatian Liberation Movement (Croatian: )", "section_idx": 8, "section_name": "Other uses", "target_page_ids": [ 3570263 ], "anchor_spans": [ [ 1, 29 ] ] }, { "plaintext": " Heritage of Pride, or HOP, the organizer of the annual gay pride march in New York City", "section_idx": 8, "section_name": "Other uses", "target_page_ids": [ 4221177 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Higher-Order Perl, or HOP, a Perl programming book", "section_idx": 8, "section_name": "Other uses", "target_page_ids": [ 4919855 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Hillsboro Hops, a minor league baseball team in the USA", "section_idx": 8, "section_name": "Other uses", "target_page_ids": [ 37363550 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Slang for Opium, heroin, or other narcotic or psychoactive drugs", "section_idx": 8, "section_name": "Other uses", "target_page_ids": [ 22713, 14034, 38079, 33632441 ], "anchor_spans": [ [ 11, 16 ], [ 18, 24 ], [ 35, 43 ], [ 47, 59 ] ] }, { "plaintext": " Hopper (disambiguation)", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 502123 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Hopping (disambiguation)", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 4170901 ], "anchor_spans": [ [ 1, 25 ] ] }, { "plaintext": " Hopps", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 21264016 ], "anchor_spans": [ [ 1, 6 ] ] }, { "plaintext": " Hip hop", "section_idx": 9, "section_name": "See also", "target_page_ids": [ 18945847 ], "anchor_spans": [ [ 1, 8 ] ] } ]

[ "Lists_of_people_by_nickname" ]

[]

[ { "plaintext": "Horn most often refers to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": "Horn (acoustic), a conical or bell shaped aperture used to guide sound", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 3247450 ], "anchor_spans": [ [ 0, 15 ] ] }, { "plaintext": " Horn (instrument), collective name for tube-shaped wind musical instruments", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 46734063 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": "Horn (anatomy), a pointed, bony projection on the head of various animals, either the \"true\" horn, or other horn-like growths", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 1243767 ], "anchor_spans": [ [ 0, 14 ] ] }, { "plaintext": " Horn, a colloquial reference to keratin, the substance that is the main component of the tissue that sheaths the bony core of horns and hoofs of various animals", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [ 43377 ], "anchor_spans": [ [ 33, 40 ] ] }, { "plaintext": "Horn may also refer to:", "section_idx": 0, "section_name": "Introduction", "target_page_ids": [], "anchor_spans": [] }, { "plaintext": " Horn loudspeaker", "section_idx": 1, "section_name": "Audio", "target_page_ids": [ 816290 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Vehicle horn", "section_idx": 1, "section_name": "Audio", "target_page_ids": [ 25409626 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Train horn", "section_idx": 1, "section_name": "Audio", "target_page_ids": [ 9330997 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Horn (surname)", "section_idx": 2, "section_name": "Personal name", "target_page_ids": [ 6720999 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Freyja, also known as Hörn, a Norse goddess of love, beauty, fertility, war and death", "section_idx": 2, "section_name": "Personal name", "target_page_ids": [ 11038 ], "anchor_spans": [ [ 1, 7 ] ] }, { "plaintext": " Cape Horn, the southernmost point of South America", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 4460850 ], "anchor_spans": [ [ 1, 10 ] ] }, { "plaintext": " Horn of Africa, a peninsula in northeast Africa", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 62142 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Horn (district), a district of the state of Lower Austria in Austria", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 5446569 ], "anchor_spans": [ [ 1, 16 ] ] }, { "plaintext": " Horn, Austria, a small town, capital of the Horn District", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 187517 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Horn, Germany, a municipality in Rhineland-Palatinate, Germany", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 13016339 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Horn, Hamburg, a quarter in the borough Hamburg-Mitte, in the eastern part of Hamburg, Germany", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 21759372 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Horn (Netherlands), a town in the Dutch province of Limburg, and a separate municipality until 1991", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 4037340 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " Horn, Oppland, a ferry docking point on the east side of Randsfjorden, a lake in Norway", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 1452403 ], "anchor_spans": [ [ 58, 70 ] ] }, { "plaintext": " Horn, Rutland, a civil parish in the East Midlands of England", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 2231753 ], "anchor_spans": [ [ 1, 14 ] ] }, { "plaintext": " Horn, Sweden, a locality", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 22444743 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Horn, Switzerland, a municipality in the district in the canton of Thurgau", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 6380211 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Horn, Nebraska, a community in the United States", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 43468573 ], "anchor_spans": [ [ 1, 15 ] ] }, { "plaintext": " Horn Island, Queensland, one of the Torres Strait Islands", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 2443406 ], "anchor_spans": [ [ 1, 24 ] ] }, { "plaintext": " Horn River, Northwest Territories, Canada ", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 22339499 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Horn (Schwarzbach), a river in eastern France and southwestern Germany", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 40226063 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " The Horn (Mount Buffalo), a peak in Victoria, Australia", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 20095719 ], "anchor_spans": [ [ 1, 25 ] ] }, { "plaintext": " The Horn (New Hampshire), a peak in the northeastern United States", "section_idx": 3, "section_name": "Places", "target_page_ids": [ 10798316 ], "anchor_spans": [ [ 1, 25 ] ] }, { "plaintext": " Horn (album), an album by Pharaoh Overlord", "section_idx": 4, "section_name": "Music", "target_page_ids": [ 30741426 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Horn (Apink album), 2022", "section_idx": 4, "section_name": "Music", "target_page_ids": [ 69895818 ], "anchor_spans": [ [ 1, 19 ] ] }, { "plaintext": " \"The Horn\", a song from the album Love Kraft by Super Furry Animals", "section_idx": 4, "section_name": "Music", "target_page_ids": [ 2386406 ], "anchor_spans": [ [ 35, 45 ] ] }, { "plaintext": " \"The Horn\", from the album Derek and Clive Ad Nauseam, a comedy track by Derek and Clive", "section_idx": 4, "section_name": "Music", "target_page_ids": [ 1504756 ], "anchor_spans": [ [ 28, 54 ] ] }, { "plaintext": "Telephone, also known as \"the horn\"", "section_idx": 5, "section_name": "Slang", "target_page_ids": [ 30003 ], "anchor_spans": [ [ 0, 9 ] ] }, { "plaintext": "Two-way radio, also known as \"the horn\"", "section_idx": 5, "section_name": "Slang", "target_page_ids": [ 804074 ], "anchor_spans": [ [ 0, 13 ] ] }, { "plaintext": " Horn (Chinese constellation), part of the European constellation Virgo", "section_idx": 6, "section_name": "Other uses", "target_page_ids": [ 3002478 ], "anchor_spans": [ [ 1, 29 ] ] }, { "plaintext": " Horn (diacritic), a diacritic mark used to indicate that a normally rounded vowel such as o or u is to be pronounced unrounded", "section_idx": 6, "section_name": "Other uses", "target_page_ids": [ 1243789 ], "anchor_spans": [ [ 1, 17 ] ] }, { "plaintext": " Horn Cable Television, a television channel in Somalia", "section_idx": 6, "section_name": "Other uses", "target_page_ids": [ 39032223 ], "anchor_spans": [ [ 1, 22 ] ] }, { "plaintext": " The knob-like appendage attached to the pommel of a saddle", "section_idx": 6, "section_name": "Other uses", "target_page_ids": [ 6373390 ], "anchor_spans": [ [ 53, 59 ] ] }, { "plaintext": " Horn antenna, a type of antenna shaped like a horn and also called \"horn\"", "section_idx": 6, "section_name": "Other uses", "target_page_ids": [ 1243766 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Glacial horn, a pyramid-shaped peak sculpted by glacial erosion", "section_idx": 6, "section_name": "Other uses", "target_page_ids": [ 654278 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Control horn, a device that helps control the control surfaces of an aircraft", "section_idx": 6, "section_name": "Other uses", "target_page_ids": [ 357636 ], "anchor_spans": [ [ 1, 13 ] ] }, { "plaintext": " Horn (video game), a mobile game", "section_idx": 6, "section_name": "Other uses", "target_page_ids": [ 43996201 ], "anchor_spans": [ [ 1, 18 ] ] }, { "plaintext": " Horned God", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 14318 ], "anchor_spans": [ [ 1, 11 ] ] }, { "plaintext": " Horns (disambiguation)", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 1274919 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Horne (disambiguation)", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 3380510 ], "anchor_spans": [ [ 1, 23 ] ] }, { "plaintext": " Hoorn (disambiguation)", "section_idx": 7, "section_name": "See also", "target_page_ids": [ 3174417 ], "anchor_spans": [ [ 1, 23 ] ] } ]

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