The single sideband version of angle modulation is defined by s (t) = exp [- (t)] cos (2ct + (t)], where (t) is

The single sideband version of angle modulation is defined by s (t) = exp [-Φ (t)] cos (2πƒct + Φ (t)], where Φ (t) is the Hilbert transform of the phase function Φ (t), and ƒc is the carrier frequency.

(a) Show that the spectrum of the modulated signal s (t) contains no frequency components in the interval –ƒc < ƒ < ƒc, and is of infinite extent.

(b) Given that the phase function Φ (t) = β sin (2πƒmt), where β is the modulation index and ƒm is the modulation frequency, derive the corresponding expression for the modulated wave s(t).