Characterization of Random Processes in Time Domain Let Y(t) = 2X(t) + sin(2t) where X(t) is a wide-sense stationary (WSS) random process with mean à = E[X(t)] = 0 and autocorrelation Rx (T) = E[X(t + 7)X(t)] = e¯|7|. (a) (5) Find the mean ÿ(t) = E[Y(t)] and the autocorrelation Ry(t +7,t) = E[Y(t + 7)Y(t)] of Y (t). (2) Is Y (t) wide-sense stationary? Why? (b) (5)Find the crosscorrelation Rxy(t+7,t) = E[X(t+7)Y(t)]. (2) Are X and Y jointly wide sense stationary? Why? (c) (5) Find the autocovariance Cy (t +7,t) = E[(Y(t + 7) − ÿ(t + 7))(Y(t) − y(t))] of Y (t). (2) Is Y (t) white? Why?
