(Solved): V (a) Show 7.15 A random process is defined as Y(t) = X(t) + X(1-T), where X (1) is a wide-sense st ...

V (a) Show 7.15 A random process is defined as Y(t) = X(t) + X(1-T), where X (1) is a wide-sense stationary random process with autocorrelation function Ry(T) and power spectral density S, (S). that Ry(t) = 2Ry(t)+ Ry(t +T) + Rx(T-T). (b) Show that Sy(f) = 4Sx (f) cos?(1 ft). (c) If X(t) has autocorrelation function Ry(t) = 5A(1), where A(T) is the unit-area triangular func- tion, and T = 0.5, find and sketch the power spec- tral density of Y(t) as defined in the problem statement.