Theory
If the baseband data signal (the message) to be transmitted is and the sinusoidal carrier is, 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:
In this equation, is the instantaneous frequency of the oscillator and is the frequency deviation, which represents the maximum shift away from fc in one direction, assuming xm(t) is limited to the range ±1.
While most of the energy of the signal is contained within fc ± fΔ, it can be shown by Fourier analysis that a wider range of frequencies is required to precisely represent an FM signal. The frequency spectrum of an actual FM signal has components extending infinitely, although their amplitude decreases and higher-order components are often neglected in practical design problems.
Read more about this topic: Frequency Modulation
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