Consider a signal x(n) = s(n) + (n), where s(n) is an AR(1) process that satisfies the

Consider a signal x(n) = s(n) + ω(n), where s(n) is an AR(1) process that satisfies the difference equation

s(n) = 0.8s(n – 1) + v(n)

where {v(n)} is a white noise sequence with variance σ²_u = 0.49 and {ω(n)} are uncorrelated.

(a) Determine the autocorrelation sequences {γ_ss(m)} and {γ_xx(m)}.

(b) Design Wiener filter of length M = 2 to estimate {s(n)}.

(c) Determine the MMSE for M = 2.