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In frequency modulation, the carrier frequency is varied upon the amplitude of the modulating frquency (information signal) without affecting the carrier's amplitude. As the modulating signal reaches the maximum peak amplitude, the carrier frequency is at it maximum, and if the modulating signal reaches the lowest peak (negative cycle), the carrier frequency is at minimum. In other words the carrier frequency is dependent on the paek amplitude of the modulating signal (information signal) hence its name, frequency modulation.
If the signal to be sent is
and the sinusoidal carrier is
xc(t) = Acos(2πfct)
where fc is the carrier's base frequency in hertz and A is an arbitrary amplitude, the carrier will be modulated by the signal as in
the frequency of the modulating signal in FM determines how fast the frequency of the carrier signal changes. the frequency of the modulating signal also produces the sidebands of the FM signal. theoretically, a single frequency modulating a carrier signal, in FM, would result to an infinite number of sidebands. but in practice, only a number of significant sidebands are taken and sent through the transmitter.