Phase modulation

It encodes a message signal as variations in the instantaneous phase of a carrier wave.

Phase modulation is an integral part of many digital transmission coding schemes that underlie a wide range of technologies like Wi-Fi, GSM and satellite television.

It is also used for signal and waveform generation in digital synthesizers, such as the Yamaha DX7, to implement FM synthesis.

A related type of sound synthesis called phase distortion is used in the Casio CZ synthesizers.

The functional form of the cosine term, which contains the expression of the instantaneous phase

[2] In FM the message signal causes a functional variation of the carrier frequency.

(phase angle) of the carrier is controlled by the modulating waveform, such that the principal frequency remains constant.

The modulating wave ( blue ) is modulating the carrier wave ( red ), resulting the PM signal ( green ).
g ( t ) = ⁠ π / 2 ⁠ ×sin[ 2×2 π t + ⁠ π / 2 ⁠ ×sin( 3×2 π t ) ]