angle modulation
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Angle modulation is a class of carrier modulation that is used in
telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that fe ...
s transmission systems. The class comprises
frequency modulation Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing. In analog fre ...
(FM) and
phase modulation Phase modulation (PM) is a modulation pattern for conditioning communication signals for transmission. It encodes a message signal as variations in the instantaneous phase of a carrier wave. Phase modulation is one of the two principal forms of ...
(PM), and is based on altering the
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
or the
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
, respectively, of a
carrier signal In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has ...
to encode the message signal. This contrasts with varying the
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
of the carrier, practiced in amplitude modulation (AM) transmission, the earliest of the major modulation methods used widely in early radio broadcasting.


Foundation

In general form, an analog modulation process of a sinusoidal carrier wave may be described by the following equation: :m(t) = A(t) \cdot \cos(\omega t + \phi(t))\,. ''A(t)'' represents the time-varying amplitude of the sinusoidal carrier wave and the cosine-term is the carrier at its circular frequency \omega, and the instantaneous phase deviation \phi(t). This description directly provides the two major groups of modulation, amplitude modulation and angle modulation. In amplitude modulation, the angle term is held constant, while in angle modulation the term ''A(t)'' is constant and the second term of the equation has a functional relationship to the modulating message signal. The functional form of the cosine term, which contains the expression of the
instantaneous phase Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a ''comple ...
\omega t + \phi(t) as its argument, provides the distinction of the two types of angle modulation,
frequency modulation Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing. In analog fre ...
(FM) and
phase modulation Phase modulation (PM) is a modulation pattern for conditioning communication signals for transmission. It encodes a message signal as variations in the instantaneous phase of a carrier wave. Phase modulation is one of the two principal forms of ...
(PM). In FM the message signal causes a functional variation of the
carrier frequency In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a ...
. These variations are controlled by both the frequency and the amplitude of the modulating wave. In phase modulation, the instantaneous phase deviation \phi(t) of the carrier is controlled by the modulating waveform, such that the principal frequency remains constant. For frequency modulation, the
instantaneous frequency Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a ''comple ...
of an angle-modulated carrier wave is given by the first derivative with respect to time of the instantaneous phase: : \frac \omega t + \phi(t) = \omega + \phi'(t) \,\!, in which \phi'(t) may be defined as the instantaneous frequency deviation, measured in rad/s. In principle, the modulating signal in both frequency and phase modulation may either be analog in nature, or it may be digital. In general, however, when using digital signals to modify the carrier wave, the method is called '' keying'', rather than modulation. Thus, telecommunications
modem A modulator-demodulator or modem is a computer hardware device that converts data from a digital format into a format suitable for an analog transmission medium such as telephone or radio. A modem transmits data by Modulation#Digital modulati ...
s use frequency-shift keying (FSK), phase-shift keying (PSK), or amplitude-phase keying (APK), or various combinations. Furthermore, another digital modulation is
line coding In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained co ...
, which uses a
baseband In telecommunications and signal processing, baseband is the range of frequencies occupied by a signal that has not been modulated to higher frequencies. Baseband signals typically originate from transducers, converting some other variable int ...
carrier, rather than a
passband A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenn ...
wave. The methods of angle modulation can provide better discrimination against interference and noise than amplitude modulation.Simon Haykin, ''Communication Systems'', John Wiley & Sons (2001), , p.107 These improvements, however, are a tradeoff against increased bandwidth requirements.


Frequency modulation

Frequency modulation Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing. In analog fre ...
is widely used for
FM broadcasting FM broadcasting is a method of radio broadcasting using frequency modulation (FM). Invented in 1933 by American engineer Edwin Armstrong, wide-band FM is used worldwide to provide high fidelity sound over broadcast radio. FM broadcasting is cap ...
of
radio programming Radio programming is the process of organising a schedule of radio content for commercial broadcasting and public broadcasting by radio stations. History The original inventors of radio, from Guglielmo Marconi's time on, expected it to be use ...
, and largely supplanted amplitude modulation for this purpose starting in the 1930s, with its invention by American engineer Edwin Armstrong in 1933. FM also has many other applications, such as in
two-way radio A two-way radio is a radio that can both transmit and receive radio waves (a transceiver), unlike a broadcast receiver which only receives content. It is an audio (sound) transceiver, a transmitter and receiver in one unit, used for bidirection ...
communications, and in
FM synthesis Frequency modulation synthesis (or FM synthesis) is a form of sound synthesis whereby the frequency of a waveform is changed by modulating its frequency with a modulator. The frequency of an oscillator is altered "in accordance with the amplitud ...
for music synthesizers.


Phase modulation

Phase modulation Phase modulation (PM) is a modulation pattern for conditioning communication signals for transmission. It encodes a message signal as variations in the instantaneous phase of a carrier wave. Phase modulation is one of the two principal forms of ...
is important in major application areas including cellular and satellite telecommunications, as well as in data networking methods, such as in some digital subscriber line systems, and
WiFi Wi-Fi () is a family of wireless network protocols, based on the IEEE 802.11 family of standards, which are commonly used for local area networking of devices and Internet access, allowing nearby digital devices to exchange data by radio wa ...
. The combination of phase modulation with amplitude modulation, practiced as early as 1874 by
Thomas Edison Thomas Alva Edison (February 11, 1847October 18, 1931) was an American inventor and businessman. He developed many devices in fields such as electric power generation, mass communication, sound recording, and motion pictures. These inventi ...
in the
quadruplex telegraph The Quadruplex telegraph is a type of electrical telegraph which allows a total of four separate signals to be transmitted and received on a single wire at the same time (two signals in each direction). Quadruplex telegraphy thus implements a fo ...
for transmitting four signals, two each in both directions of transmission, constitutes the
polar modulation Polar modulation is analogous to quadrature modulation in the same way that polar coordinates are analogous to Cartesian coordinates. Quadrature modulation makes use of Cartesian coordinates, ''x'' and ''y''. When considering quadrature modulat ...
technique.


References

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Further reading

*Bell Telephone Laboratories, ''Transmission Systems for Communications'', 5th Edition, Holmdel, NJ, 1982, Chapter 6—''Signal Conditioning'', p.93. Radio modulation modes