Narrowband and wideband frequency modulation spectral characterization and bandwidth calculation

Frequency modulation (FM) is a class of analog modulation techniques that rely on varying the instantaneous frequency of a radio-frequency (RF) carrier in accordance with the baseband signal. The amplitude of the FM signal is constant, while its instantaneous frequency is time variant; therefore, the zero crossing rate (ZCR) of the carrier differs at a rate proportional to the Nyquist rate of the baseband signal. Unlike amplitude modulation (AM), FM is a nonlinear modulation technique; therefore, the calculation of the spectrum of an FM signal is expected to be a tedious mathematical problem.