Using the given information, please help me solve the following:

PROBLEM 1(20pts) Consider a measurement process, x, = s, + n, that is the sum of a signal that is statistically independent of the noise, and where the signal and noise processes are: Signal: s, is an AR(2) process s, = -dis -1-d2s,-2 tu, ; Noise: n, is an AR(1) process: n, = -bin -1 + v. For an ARMA(n,m) process of the form: x, = - m ak* * - * + bKWIK ; bo =1 where w, is white with power o? k=1 k=0 n then X(z) = G(z)W(z), where G(z) = B(z) / A(z) with A(z) = _axz-k & B(z) m -k A ; a=1. K=0 k=0 Hence, for z = e' the Wiener-Kintchine Theorem gives S, (@) =| G(ei@) 2 62