Angle modulation is a class of signal modulation that is used in telecommunication transmission systems using carrier waves. The class comprises frequency modulation (FM) and phase modulation (PM), and is based on altering the frequency or the phase, respectively, of a carrier signal to encode the message signal. This contrasts with varying the amplitude of the carrier, practiced in amplitude 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:

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

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

in which ${\displaystyle \phi '(t)}$ 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 ${\displaystyle \phi _{FM}'=K_{FM}s(t),}$ which gives the FM modulated waveform as

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