Two zero- mean discrete random processes, X [n] and Y [n], are statistically independent and have autocorrelation functions given by RXX [k] = (1/ 2) k and RYY [k] = (1/ 3) k . Let a new random process be Z [n] = X [n] + Y [n].
(a) Find RZZ [k]. Plot all three autocorrelation functions.
(b) Determine all three PSD functions analytically and plot the PSDs.