# Frequency modulation

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In telecommunications and signal processing, frequency modulation (FM) conveys information over a carrier wave by varying its instantaneous frequency (contrast this with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant). In analog applications, the difference between the instantaneous and the base frequency of the carrier is directly proportional to the instantaneous value of the input signal amplitude. Digital data can be sent by shifting the carrier's frequency among a set of discrete values, a technique known as frequency-shift keying.

Frequency modulation can be regarded as phase modulation where the carrier phase modulation is the time integral of the FM modulating signal.

## Contents

### Theory

Suppose the baseband data signal (the message) to be transmitted is xm(t) and the sinusoidal carrier is $x_c(t) = A_c \cos (2 \pi f_c t)\,$, where fc is the carrier's base frequency and Ac is the carrier's amplitude. The modulator combines the carrier with the baseband data signal to get the transmitted signal: