Suppose that the received signal is an FM system contains some residual amplitude modulation of positive amplitude a (t), as shown by s (t) = a (t) cos [2??_ct + ? (t)], where ?c is the carrier frequency. The phase ? (t) is related to the modulating signal m (t) by, where k_? is a constant. Assume that the signal s (t) is restricted to a frequency band of width BT, centered at ?_c, where BT is the transmission bandwidth of the FM signal in the absence of amplitude modulation, and the amplitude modulation is slowly varying compared with ? (t). Show that the output of an ideal frequency discriminator produced by s (t) is proportional to a (t) m (t).

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