General Services Administration
The General Services Administration, an independent agency of the United States government, was established in 1949 to help manage and support the basic functioning of federal agencies. GSA supplies products and communications for U. S. government offices, provides transportation and office space to federal employees, develops government-wide cost-minimizing policies and other management tasks. GSA employs about 12,000 federal workers and has an annual operating budget of $20.9 billion. GSA oversees $66 billion of procurement annually, it contributes to the management of about $500 billion in U. S. federal property, divided chiefly among 8,700 owned and leased buildings and a 215,000 vehicle motor pool. Among the real estate assets managed by GSA are the Ronald Reagan Building and International Trade Center in Washington, D. C. – the largest U. S. federal building after the Pentagon – and the Hart-Dole-Inouye Federal Center. GSA's business lines include the Federal Acquisition Service and the Public Buildings Service, as well as several Staff Offices including the Office of Government-wide Policy, the Office of Small Business Utilization, the Office of Mission Assurance.
As part of FAS, GSA's Technology Transformation Services helps federal agencies improve delivery of information and services to the public. Key initiatives include FedRAMP, Cloud.gov, the USAGov platform, Data.gov, Performance.gov, Challenge.gov. GSA is a member of the Procurement G6, an informal group leading the use of framework agreements and e-procurement instruments in public procurement. In 1947 President Harry Truman asked former President Herbert Hoover to lead what became known as the Hoover Commission to make recommendations to reorganize the operations of the federal government. One of the recommendations of the commission was the establishment of an "Office of the General Services." This proposed office would combine the responsibilities of the following organizations: U. S. Treasury Department's Bureau of Federal Supply U. S. Treasury Department's Office of Contract Settlement National Archives Establishment All functions of the Federal Works Agency, including the Public Buildings Administration and the Public Roads Administration War Assets AdministrationGSA became an independent agency on July 1, 1949, after the passage of the Federal Property and Administrative Services Act.
General Jess Larson, Administrator of the War Assets Administration, was named GSA's first Administrator. The first job awaiting Administrator Larson and the newly formed GSA was a complete renovation of the White House; the structure had fallen into such a state of disrepair by 1949 that one inspector of the time said the historic structure was standing "purely from habit." Larson explained the nature of the total renovation in depth by saying, "In order to make the White House structurally sound, it was necessary to dismantle, I mean dismantle, everything from the White House except the four walls, which were constructed of stone. Everything, except the four walls without a roof, was stripped down, that's where the work started." GSA worked with President Truman and First Lady Bess Truman to ensure that the new agency's first major project would be a success. GSA completed the renovation in 1952. In 1986 GSA headquarters, U. S. General Services Administration Building, located at Eighteenth and F Streets, NW, was listed on the National Register of Historic Places, at the time serving as Interior Department offices.
In 1960 GSA created the Federal Telecommunications System, a government-wide intercity telephone system. In 1962 the Ad Hoc Committee on Federal Office Space created a new building program to address obsolete office buildings in Washington, D. C. resulting in the construction of many of the offices that now line Independence Avenue. In 1970 the Nixon administration created the Consumer Product Information Coordinating Center, now part of USAGov. In 1974 the Federal Buildings Fund was initiated, allowing GSA to issue rent bills to federal agencies. In 1972 GSA established the Automated Data and Telecommunications Service, which became the Office of Information Resources Management. In 1973 GSA created the Office of Federal Management Policy. GSA's Office of Acquisition Policy centralized procurement policy in 1978. GSA was responsible for emergency preparedness and stockpiling strategic materials to be used in wartime until these functions were transferred to the newly-created Federal Emergency Management Agency in 1979.
In 1984 GSA introduced the federal government to the use of charge cards, known as the GMA SmartPay system. The National Archives and Records Administration was spun off into an independent agency in 1985; the same year, GSA began to provide governmentwide policy oversight and guidance for federal real property management as a result of an Executive Order signed by President Ronald Reagan. In 2003 the Federal Protective Service was moved to the Department of Homeland Security. In 2005 GSA reorganized to merge the Federal Supply Service and Federal Technology Service business lines into the Federal Acquisition Service. On April 3, 2009, President Barack Obama nominated Martha N. Johnson to serve as GSA Administrator. After a nine-month delay, the United States Senate confirmed her nomination on February 4, 2010. On April 2, 2012, Johnson resigned in the wake of a management-deficiency report that detailed improper payments for a 2010 "Western Regions" training conference put on by the Public Buildings Service in Las Vegas.
In July 1991 GSA contractors began the excavation of what is now the Ted Weiss Federal Building in New York City. The planning for that buildin
In electronics and telecommunications, a transmitter or radio transmitter is an electronic device which produces radio waves with an antenna. The transmitter itself generates a radio frequency alternating current, applied to the antenna; when excited by this alternating current, the antenna radiates radio waves. Transmitters are necessary component parts of all electronic devices that communicate by radio, such as radio and television broadcasting stations, cell phones, walkie-talkies, wireless computer networks, Bluetooth enabled devices, garage door openers, two-way radios in aircraft, spacecraft, radar sets and navigational beacons; the term transmitter is limited to equipment that generates radio waves for communication purposes. Generators of radio waves for heating or industrial purposes, such as microwave ovens or diathermy equipment, are not called transmitters though they have similar circuits; the term is popularly used more to refer to a broadcast transmitter, a transmitter used in broadcasting, as in FM radio transmitter or television transmitter.
This usage includes both the transmitter proper, the antenna, the building it is housed in. A transmitter can be a separate piece of electronic equipment, or an electrical circuit within another electronic device. A transmitter and a receiver combined in one unit is called a transceiver; the term transmitter is abbreviated "XMTR" or "TX" in technical documents. The purpose of most transmitters is radio communication of information over a distance; the information is provided to the transmitter in the form of an electronic signal, such as an audio signal from a microphone, a video signal from a video camera, or in wireless networking devices, a digital signal from a computer. The transmitter combines the information signal to be carried with the radio frequency signal which generates the radio waves, called the carrier signal; this process is called modulation. The information can be added to the carrier in several different ways, in different types of transmitters. In an amplitude modulation transmitter, the information is added to the radio signal by varying its amplitude.
In a frequency modulation transmitter, it is added by varying the radio signal's frequency slightly. Many other types of modulation are used; the radio signal from the transmitter is applied to the antenna, which radiates the energy as radio waves. The antenna may be enclosed inside the case or attached to the outside of the transmitter, as in portable devices such as cell phones, walkie-talkies, garage door openers. In more powerful transmitters, the antenna may be located on top of a building or on a separate tower, connected to the transmitter by a feed line, a transmission line. Electromagnetic waves are radiated by electric charges undergoing acceleration. Radio waves, electromagnetic waves of radio frequency, are generated by time-varying electric currents, consisting of electrons flowing through a metal conductor called an antenna which are changing their velocity or direction and thus accelerating. An alternating current flowing back and forth in an antenna will create an oscillating magnetic field around the conductor.
The alternating voltage will charge the ends of the conductor alternately positive and negative, creating an oscillating electric field around the conductor. If the frequency of the oscillations is high enough, in the radio frequency range above about 20 kHz, the oscillating coupled electric and magnetic fields will radiate away from the antenna into space as an electromagnetic wave, a radio wave. A radio transmitter is an electronic circuit which transforms electric power from a power source into a radio frequency alternating current to apply to the antenna, the antenna radiates the energy from this current as radio waves; the transmitter impresses information such as an audio or video signal onto the radio frequency current to be carried by the radio waves. When they strike the antenna of a radio receiver, the waves excite similar radio frequency currents in it; the radio receiver extracts the information from the received waves. A practical radio transmitter consists of these parts: A power supply circuit to transform the input electrical power to the higher voltages needed to produce the required power output.
An electronic oscillator circuit to generate the radio frequency signal. This generates a sine wave of constant amplitude called the carrier wave, because it serves to "carry" the information through space. In most modern transmitters, this is a crystal oscillator in which the frequency is controlled by the vibrations of a quartz crystal; the frequency of the carrier wave is considered the frequency of the transmitter. A modulator circuit to add the information to be transmitted to the carrier wave produced by the oscillator; this is done by varying some aspect of the carrier wave. The information is provided to the transmitter either in the form of an audio signal, which represents sound, a video signal which represents moving images, or for data in the form of a binary digital signal which represents a sequence of bits, a bitstream. Different types of transmitters use different modulation methods to transmit information: In an AM transmitter the amplitude of the carrier wave is varied in proportion to the modulation signal.
In an FM transmitter the frequency of the carrier is varied by the modulation signal. In an FSK transmitter, which transmits digital data, the frequency of the carrier is shifted between two frequencies which represent the two binary digits, 0 and 1. Many oth
John Renshaw Carson
John Renshaw Carson was a noted transmission theorist for early communications systems. He invented single-sideband modulation and developed the Carson bandwidth rule for estimating frequency modulation bandwidth. In 2013 Carson was inducted into the Electronic Design Hall of Fame for his contributions to communications. Carson was born in Pittsburgh and together with his twin brother Joseph attended Princeton University, graduating in 1907 with a Bachelor of Science degree. John attended the Massachusetts Institute of Technology 1907–1908, before returning to Princeton to receive his electrical engineering degree in 1909 and a Master of Science degree in 1912. From 1912 to 1914 Carson was an instructor in Electrical Engineering and Physics at Princeton, but in 1913 was offered a position at American Telephone & Telegraph, in 1914 left the university. At AT&T, Carson was involved in early radio telephone experiments. In 1915 he invented single-sideband modulation to transmit multiple telephone calls on a single electrical circuit, was responsible for installing the first such system between Pittsburgh and Baltimore.
In 1922 he published a mathematical treatment of frequency modulation, which introduced the Carson bandwidth rule. In his 1922 paper, Carson presented a negative opinion of narrowband FM, which occurs when the maximum frequency swing is made narrower than the audio bandwidth. Edwin Armstrong managed to demonstrate that FM can be advantageous if the frequency swing is wider than the audio bandwidth. From 1917 to 1925 Carson analyzed the effects of filters on amplitude modulation via operational calculus, thus allowing telephone system designers to predict crosstalk in multiple calls over a single pair of wires, he published a series of papers on this subject in the Bell System Technical Journal, culminating in his 1926 book Electrical Circuit Theory and Operational Calculus. From 1925 to 1940 Carson worked for Bell Telephone Laboratories as a mathematician and electrical engineer. Notable work during this era included his mathematical analysis of George C. Southworth's 1932 waveguide experiments.
Carson received the 1924 IRE Morris N. Liebmann Memorial Award "in recognition of his valuable contributions to alternating current circuit theory and, in particular, to his investigations of filter systems and of single side band telephony." He received an honorary Doctor of Science degree from Brooklyn Polytechnic Institute in 1937, the 1939 Elliott Cresson Medal from the Franklin Institute. His undergraduate letters are archived at Princeton University. U. S. Patent 1,449,382: John Carson/AT&T: "Method and Means for Signaling with High Frequency Waves" filed on December 1, 1915. 1922: "Notes on the Theory of Modulation", Proceedings of the Institute of Radio Engineers, volume 10, issue 1, pages 57–64. 1924: A Generalization of Reciprocal Theorem, Bell System Technical Journal 3: 393–399. 1925: Selective Circuits and Static Interference, Bell System Technical Journal, 4:265. 1926: Wave Propagation in Overhead Wires with Ground Return, Bell System Technical Journal, 5: 539. 1926: Electrical Circuit Theory and Operational Calculus, New York: McGraw–Hill.
1926: The Heaviside Operational Calculus, Bulletin of the American Mathematical Society 32:43–68, link from Project Euclid. 1936: Hyper-Frequency Waveguides: Mathematical Theory, Bell System Technical Journal 15: 310–333. Laplace–Carson transform John & Robb Carson Letters in Mudd Manuscript Library of Princeton University Library Archives. Brittain, J. E. "John R. Carson and the conservation of radio spectrum", Proceedings of the IEEE, volume 84, issue 6, June 1996, pages 909–910. Mario Lucertini, Ana Millán Gasca, F. Nicolò, Technological Concepts and Mathematical Models in the Evolution of Modern Engineering Systems, Birkhäuser, 2004, pages 114–117. ISBN 3-7643-6940-X. Julie K. Petersen, Fiber Optics Illustrated Dictionary, CRC Press, 2003, page 264. ISBN 0-8493-1349-X
In radio communications, a radio receiver known as a receiver, wireless or radio is an electronic device that receives radio waves and converts the information carried by them to a usable form. It is used with an antenna; the antenna intercepts radio waves and converts them to tiny alternating currents which are applied to the receiver, the receiver extracts the desired information. The receiver uses electronic filters to separate the desired radio frequency signal from all the other signals picked up by the antenna, an electronic amplifier to increase the power of the signal for further processing, recovers the desired information through demodulation; the information produced by the receiver may be in the form of sound, moving data. A radio receiver may be a separate piece of electronic equipment, or an electronic circuit within another device. Radio receivers are widely used in modern technology, as components of communications, remote control, wireless networking systems. In consumer electronics, the terms radio and radio receiver are used for receivers designed to reproduce sound transmitted by radio broadcasting stations the first mass-market commercial radio application.
The most familiar form of radio receiver is a broadcast receiver just called a radio, which receives audio programs intended for public reception transmitted by local radio stations. The sound is reproduced either by a loudspeaker in the radio or an earphone which plugs into a jack on the radio; the radio requires electric power, provided either by batteries inside the radio or a power cord which plugs into an electric outlet. All radios have a volume control to adjust the loudness of the audio, some type of "tuning" control to select the radio station to be received. Modulation is the process of adding information to a radio carrier wave. Two types of modulation are used in analog radio broadcasting systems. In amplitude modulation the strength of the radio signal is varied by the audio signal. AM broadcasting is allowed in the AM broadcast bands which are between 148 and 283 kHz in the longwave range, between 526 and 1706 kHz in the medium frequency range of the radio spectrum. AM broadcasting is permitted in shortwave bands, between about 2.3 and 26 MHz, which are used for long distance international broadcasting.
In frequency modulation the frequency of the radio signal is varied by the audio signal. FM broadcasting is permitted in the FM broadcast bands between about 65 and 108 MHz in the high frequency range; the exact frequency ranges vary somewhat in different countries. FM stereo radio stations broadcast in stereophonic sound, transmitting two sound channels representing left and right microphones. A stereo receiver contains the additional circuits and parallel signal paths to reproduce the two separate channels. A monaural receiver, in contrast, only receives a single audio channel, a combination of the left and right channels. While AM stereo transmitters and receivers exist, they have not achieved the popularity of FM stereo. Most modern radios are "AM/FM" radios, are able to receive both AM and FM radio stations, have a switch to select which band to receive. Digital audio broadcasting is an advanced radio technology which debuted in some countries in 1998 that transmits audio from terrestrial radio stations as a digital signal rather than an analog signal as AM and FM do.
Its advantages are that DAB has the potential to provide higher quality sound than FM, has greater immunity to radio noise and interference, makes better use of scarce radio spectrum bandwidth, provides advanced user features such as electronic program guide, sports commentaries, image slideshows. Its disadvantage is that it is incompatible with previous radios so that a new DAB receiver must be purchased; as of 2017, 38 countries offer DAB, with 2,100 stations serving listening areas containing 420 million people. Most countries plan an eventual switchover from FM to DAB; the United States and Canada have chosen not to implement DAB. DAB radio stations work differently from AM or FM stations: a single DAB station transmits a wide 1,500 kHz bandwidth signal that carries from 9 to 12 channels from which the listener can choose. Broadcasters can transmit a channel at a range of different bit rates, so different channels can have different audio quality. In different countries DAB stations broadcast in either Band L band.
The signal strength of radio waves decreases the farther they travel from the transmitter, so a radio station can only be received within a limited range of its transmitter. The range depends on the power of the transmitter, the sensitivity of the receiver and internal noise, as well as any geographical obstructions such as hills between transmitter and receiver. AM broadcast band radio waves travel as ground waves which follow the contour of the Earth, so AM radio stations can be reliably received at hundreds of miles distance. Due to their higher frequency, FM band radio signals cannot travel far beyond the visual horizon; however FM radio has higher fidelity. So in many countries serious music is only broadcast by FM stations, AM stations specialize in radio news, talk radio, sports. Like FM, DAB signals travel by line of sight so reception distances are
Telecommunication is the transmission of signs, messages, writings and sounds or information of any nature by wire, optical or other electromagnetic systems. Telecommunication occurs when the exchange of information between communication participants includes the use of technology, it is transmitted either electrically over physical media, such as cables, or via electromagnetic radiation. Such transmission paths are divided into communication channels which afford the advantages of multiplexing. Since the Latin term communicatio is considered the social process of information exchange, the term telecommunications is used in its plural form because it involves many different technologies. Early means of communicating over a distance included visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, optical heliographs. Other examples of pre-modern long-distance communication included audio messages such as coded drumbeats, lung-blown horns, loud whistles. 20th- and 21st-century technologies for long-distance communication involve electrical and electromagnetic technologies, such as telegraph and teleprinter, radio, microwave transmission, fiber optics, communications satellites.
A revolution in wireless communication began in the first decade of the 20th century with the pioneering developments in radio communications by Guglielmo Marconi, who won the Nobel Prize in Physics in 1909, other notable pioneering inventors and developers in the field of electrical and electronic telecommunications. These included Charles Wheatstone and Samuel Morse, Alexander Graham Bell, Edwin Armstrong and Lee de Forest, as well as Vladimir K. Zworykin, John Logie Baird and Philo Farnsworth; the word telecommunication is a compound of the Greek prefix tele, meaning distant, far off, or afar, the Latin communicare, meaning to share. Its modern use is adapted from the French, because its written use was recorded in 1904 by the French engineer and novelist Édouard Estaunié. Communication was first used as an English word in the late 14th century, it comes from Old French comunicacion, from Latin communicationem, noun of action from past participle stem of communicare "to share, divide out.
Homing pigeons have been used throughout history by different cultures. Pigeon post had Persian roots, was used by the Romans to aid their military. Frontinus said; the Greeks conveyed the names of the victors at the Olympic Games to various cities using homing pigeons. In the early 19th century, the Dutch government used the system in Sumatra, and in 1849, Paul Julius Reuter started a pigeon service to fly stock prices between Aachen and Brussels, a service that operated for a year until the gap in the telegraph link was closed. In the Middle Ages, chains of beacons were used on hilltops as a means of relaying a signal. Beacon chains suffered the drawback that they could only pass a single bit of information, so the meaning of the message such as "the enemy has been sighted" had to be agreed upon in advance. One notable instance of their use was during the Spanish Armada, when a beacon chain relayed a signal from Plymouth to London. In 1792, Claude Chappe, a French engineer, built the first fixed visual telegraphy system between Lille and Paris.
However semaphore suffered from the need for skilled operators and expensive towers at intervals of ten to thirty kilometres. As a result of competition from the electrical telegraph, the last commercial line was abandoned in 1880. On 25 July 1837 the first commercial electrical telegraph was demonstrated by English inventor Sir William Fothergill Cooke, English scientist Sir Charles Wheatstone. Both inventors viewed their device as "an improvement to the electromagnetic telegraph" not as a new device. Samuel Morse independently developed a version of the electrical telegraph that he unsuccessfully demonstrated on 2 September 1837, his code was an important advance over Wheatstone's signaling method. The first transatlantic telegraph cable was completed on 27 July 1866, allowing transatlantic telecommunication for the first time; the conventional telephone was invented independently by Alexander Bell and Elisha Gray in 1876. Antonio Meucci invented the first device that allowed the electrical transmission of voice over a line in 1849.
However Meucci's device was of little practical value because it relied upon the electrophonic effect and thus required users to place the receiver in their mouth to "hear" what was being said. The first commercial telephone services were set-up in 1878 and 1879 on both sides of the Atlantic in the cities of New Haven and London. Starting in 1894, Italian inventor Guglielmo Marconi began developing a wireless communication using the newly discovered phenomenon of radio waves, showing by 1901 that they could be transmitted across the Atlantic Ocean; this was the start of wireless telegraphy by radio. Voice and music had little early success. World War I accelerated the development of radio for military communications. After the war, commercial radio AM broadcasting began in the 1920s and became an important mass medium for entertainment and news. World War II again accelerated development of radio for the wartime purposes of aircraft and land communication, radio navigation and radar. Development of stereo FM broadcasting of radio
In telecommunication, a communications system or communication system is a collection of individual communications networks, transmission systems, relay stations, tributary stations, data terminal equipment capable of interconnection and interoperation to form an integrated whole. The components of a communications system serve a common purpose, are technically compatible, use common procedures, respond to controls, operate in union. Telecommunications is a method of communication. Communication is the act of conveying intended meanings from one entity or group to another through the use of mutually understood signs and semiotic rules An optical communication system is any form of telecommunication that uses light as the transmission medium. Equipment consists of a transmitter, which encodes a message into an optical signal, a communication channel, which carries the signal to its destination, a receiver, which reproduces the message from the received optical signal. Fiber-optic communication systems transmit information from one place to another by sending light through an optical fiber.
The light forms a carrier signal, modulated to carry information. A radio communication system is composed of several communications subsystems that give exterior communications capabilities. A radio communication system comprises a transmitting conductor in which electrical oscillations or currents are produced and, arranged to cause such currents or oscillations to be propagated through the free space medium from one point to another remote therefrom and a receiving conductor at such distant point adapted to be excited by the oscillations or currents propagated from the transmitter. Power line communication systems operate by impressing a modulated carrier signal on power wires. Different types of powerline communications use different frequency bands, depending on the signal transmission characteristics of the power wiring used. Since the power wiring system was intended for transmission of AC power, the power wire circuits have only a limited ability to carry higher frequencies; the propagation problem is a limiting factor for each type of power line communications.
A duplex communication system is a system composed of two connected parties or devices which can communicate with one another in both directions. The term duplex is used when describing communication between devices. Duplex systems are employed in nearly all communications networks, either to allow for a communication "two-way street" between two connected parties or to provide a "reverse path" for the monitoring and remote adjustment of equipment in the field. An Antenna is a small length of a qwert conductor, used to radiate or receive electromagnetic waves, it acts as a conversion device. At the transmitting end it converts high frequency current into electromagnetic waves. At the receiving end it transforms electromagnetic waves into electrical signals, fed into the input of the receiver. Several types of antenna are used in communication. Examples of communications subsystems include the Defense Communications System. Telephone Mobile Telegraph Edison Telegraph T. V. Cable Computer A tactical communications system is a communications system, used within, or in direct support of tactical forces is designed to meet the requirements of changing tactical situations and varying environmental conditions, provides securable communications, such as voice and video, among mobile users to facilitate command and control within, in support of, tactical forces, requires short installation times on the order of hours, in order to meet the requirements of frequent relocation.
An Emergency communication system is any system, organized for the primary purpose of supporting the two way communication of emergency messages between both individuals and groups of individuals. These systems are designed to integrate the cross-communication of messages between are variety of communication technologies. An Automatic call distributor is a communication system that automatically queues and connects callers to handlers; this is used in customer service, ordering by telephone, or coordination services. A Voice Communication Control System is an ACD with characteristics that make it more adapted to use in critical situations Sources can be classified as electric or non-electric. Examples of sources include but are not limited to the following: Audio Files Graphic Image Files Email Messages Human Voice Television Picture Electromagnetic Radiation Sensors, like microphones and cameras, capture non-electric sources, like sound and light, convert them into electrical signals; these types of sensors are called input transducers in modern analog and digital communication systems.
Without input transducers there would not be an effective way to transport non-electric sources or signals over great distances, i.e. humans would have to rely on our eyes and ears to see and hear things despite the distances. Not good! Other examples of input transducers include: Microphones Cameras Keyboards Mouse Force Sensors Accelerometers Once the source signal has been converted into an electric signal, the transmitter will modify this signal for efficient transmission. In order to do
In telecommunications and signal processing, frequency modulation is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. In analog frequency modulation, such as FM radio broadcasting of an audio signal representing voice or music, the instantaneous frequency deviation, the difference between the frequency of the carrier and its center frequency, is proportional to the modulating signal. Digital data can be encoded and transmitted via FM by shifting the carrier's frequency among a predefined set of frequencies representing digits – for example one frequency can represent a binary 1 and a second can represent binary 0; this modulation technique is known as frequency-shift keying. FSK is used in modems such as fax modems, can be used to send Morse code. Radioteletype uses FSK. Frequency modulation is used for FM radio broadcasting, it is used in telemetry, seismic prospecting, monitoring newborns for seizures via EEG, two-way radio systems, music synthesis, magnetic tape-recording systems and some video-transmission systems.
In radio transmission, an advantage of frequency modulation is that it has a larger signal-to-noise ratio and therefore rejects radio frequency interference better than an equal power amplitude modulation signal. For this reason, most music is broadcast over FM radio. Frequency modulation and phase modulation are the two complementary principal methods of angle modulation; these methods contrast with amplitude modulation, in which the amplitude of the carrier wave varies, while the frequency and phase remain constant. If the information to be transmitted is x m and the sinusoidal carrier is x c = A c cos , where fc is the carrier's base frequency, Ac is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal: y = A c cos = A c cos = A c cos where f Δ = K f A m, K f being the sensitivity of the frequency modulator and A m being the amplitude of the modulating signal or baseband signal. In this equation, f is the instantaneous frequency of the oscillator and f Δ is the frequency deviation, which represents the maximum shift away from fc in one direction, assuming xm is limited to the range ±1.
While most of the energy of the signal is contained within fc ± fΔ, it can be shown by Fourier analysis that a wider range of frequencies is required to represent an FM signal. The frequency spectrum of an actual FM signal has components extending infinitely, although their amplitude decreases and higher-order components are neglected in practical design problems. Mathematically, a baseband modulating signal may be approximated by a sinusoidal continuous wave signal with a frequency fm; this method is named as single-tone modulation. The integral of such a signal is: ∫ 0 t x m d τ = A m sin