Mathematical representaion of FM

Modulation is the process by which some characteristic of the carrier is varied in accordance with modulating (input) signal. FM is the modulation in which the instantaneous frequency of the carrier c(t) is varied linearly with message signal m(t). This means frequency of the carrier is changed according to amplitude of modulating signal. So, in FM message signal (baseband signal) changes the frequency of the carrier wave without changing its amplitude or phase angle.