Let M(t) be a wide sense stationary random process with average power E[M2(t)] = q and power spectral density SM ( 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)]?