Let mt be a wide sense stationary random process with

Question

Let M(t) be a wide sense stationary random process with average power E[M²(t)] = q and power spectral density S_M ( f ). The Hilbert transform of M(t) is (t), a signal obtained by passing M(t) through a linear time-invariant filter with frequency response

(a) Find the power spectral density S (f) and the average power  = E[²(t)].

(b) In a single sideband communications system, the upper sideband signal is

Where ? has a uniform PDF over [0, 2π ), independent of M(t) and Mˆ (t). What is the average power E[U²(t)]?