Probability and random processes for engineer, w(n) denotes zero-mean ergodic no

Question

Probability and random processes for engineer, w(n) denotes zero-mean ergodic noise with autocorrelation r_ww(m). x(n) = cos((2pi/N)n) middot w(n) where N is a positive integer. (a) Find the ensemble autocorrelation r_xx(m) = E[x(n) times (n + m). (b) Find the exact (no approximations) time-average autocorrelation M = 1.M sigma^M _n = 0 x(n)x(n + m) where M = k middot N (M is a multiple of N). Your answer should be simplified, using the fact that the cosine is periodic. (c) Find a simple approximation to your answer from part (b), using the fact that w(n) is ergodic (d) Is x(n) stationary? Is x(n) ergodic?

Explanation / Answer

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