Repeat Exercise 6.37 A sequence of zero mean unit variance independent random variables, Xn, n = 0,

Question:

Repeat Exercise 6.37 A sequence of zero mean unit variance independent random variables, Xn, n = 0, 1, 2, …, N – 1 are input to a filter that produces an output sequence according to Xn – Xn – 1 = (Xn + Xn – 1)/ 2, for . For n = 0, 1, 2 … N – 1.For initialization purposes, X –1 is taken to be zero.
(a) Find the covariance (correlation) matrix of the Xn – Xn – 1.
(b) Now let the variance of the Xn be σ2X. Find the covariance (correlation) matrix of the Xn – Xn – 1.