Angle modulation is a class ofsignal modulation that is used intelecommunication transmission systems usingcarrier waves. The class comprisesfrequency modulation (FM) andphase modulation (PM), and is based on altering thefrequency or thephase, respectively, of acarrier signal to encode the message signal. This contrasts with varying theamplitude of the carrier, practiced inamplitude modulation (AM) transmission, the earliest of the major modulation methods used widely in early radio broadcasting.

In general form, an analog modulation process of a sinusoidal carrier wave may be described by the following equation:^[1]

${\displaystyle m(t)=A(t)\cdot \cos (\omega t+\varphi (t))}$.

${\displaystyle A(t)}$ represents the time-varying amplitude of the sinusoidal carrier wave and the cosine-term is the carrier at itsangular frequency${\displaystyle \omega }$, and the instantaneous phase deviation${\displaystyle \varphi (t)}$. 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${\displaystyle A(t)}$ 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 theinstantaneous phase${\displaystyle \omega t+\varphi (t)}$ as its argument, provides the distinction of the two types of angle modulation,frequency modulation (FM) andphase modulation (PM).^[2] In FM the message signal causes a functional variation of theinstantaneous frequency. These variations are controlled by both the frequency and the amplitude of the modulating wave. In phase modulation, the instantaneous phase deviation${\displaystyle \varphi (t)}$ of the carrier is controlled by the modulating waveform, such that the principal frequency remains constant.

For angle modulation, theinstantaneous frequency of an angle-modulated carrier wave is given by the first derivative of the instantaneous phase with respect to time:

${\displaystyle {\omega }_I=\frac{d}{dt}[\omega t+\varphi (t)]=\omega +{\varphi }^{\prime }(t),}$

in which${\displaystyle {\varphi }^{\prime }(t)}$ may be defined as the instantaneous frequency deviation, measured in rad/s.

For frequency modulation (FM), the modulating signal${\displaystyle s(t)}$ is related linearly to the instantaneous frequency deviation, that is${\displaystyle {\varphi }_{FM}^{\prime }=K_{FM}s(t),}$ which gives the FM modulated waveform as

${\displaystyle m_{FM}(t)=A\cos \left(\omega t+K_{FM}\int s(\tau )d\tau \right).}$

For phase modulation (PM), the modulating signal${\displaystyle s(t)}$ is related linearly to the instantaneous phase deviation, that is${\displaystyle {\varphi }_{PM}(t)=K_{PM}s(t),}$ which gives the PM modulated waveform as

${\displaystyle m_{PM}(t)=A\cos \left(\omega t+K_{PM}s(t)\right).}$

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 calledkeying, rather than modulation.^[3] Thus, telecommunicationsmodems usefrequency-shift keying (FSK),phase-shift keying (PSK), oramplitude-phase keying (APK), or various combinations. Furthermore, another digital modulation isline coding, which uses abaseband carrier, rather than apassband wave.

The methods of angle modulation can provide better discrimination against interference and noise than amplitude modulation.^[2] These improvements, however, are a tradeoff against increased bandwidth requirements.

Frequency modulation is widely used forFM broadcasting ofradio programming, and largely supplanted amplitude modulation for this purpose starting in the 1930s, with its invention by American engineerEdwin Armstrong in 1933.^[4] FM also has many other applications, such as intwo-way radio communications, and inFM synthesis formusic synthesizers.

Phase modulation is important in major application areas including cellular and satellite telecommunications, as well as in data networking methods, such as in somedigital subscriber line systems, andWiFi.

The combination of phase modulation with amplitude modulation, practiced as early as 1874 byThomas Edison in thequadruplex telegraph for transmitting four signals, two each in both directions of transmission, constitutes thepolar modulation technique.

• Bell Telephone Laboratories Staff (1982). "Chapter 6—Signal Conditioning".Transmission Systems for Communications; (5 ed.). Holmdel, NJ. p. 93.{{cite book}}: CS1 maint: location missing publisher (link)

• Radio modulation modes

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