Continuing problem 1143 find the optimal filter h h0nbsph1

Question

Continuing Problem 11.4.3, find the optimal filter h = [h₀ h₁] based on M = 2 samples of Y_n. What value of c minimizes the mean square estimation error?

Problem 11.4.3

Let X_n be a wide sense stationary random sequence with expected value E[X_n] = 0 and autocorrelation function

Where |c|

Where Z_n is an iid noise sequence, independent of X_n, with E[Zn] = 0 and Var[Zn] = η². Find the LMSE estimate of X_n given Y_n and the minimum mean square estimaton error