Problem 7 We will demonstrate the connection between the signal's expected spectrum and the signal's autocor- relation function through simulation of a discrete-time system. 1. Consider a filtered zero-mean unit-variance Gaussian i.i.d. process Yn= Xn-chi, I=-00 n=-O where {Xn}n=-- is the input Gaussian i.i.d. process, h, is the impulse response of a linear time-invariant filter, and {Yn}n=-o is the filter's output process. Show that the autocorrelation of the output process is given by Ry [m] := E[Yn Yn+m] = . = t- hi hm+1 I=-00 In particular, if h = 0 for 1 L, then min(L,L-m) Ry [m] = l=max(0,m) hihm+10 = 2. We simulate Yn with Matlab. As an example of the LTI filter, let hi = [+1 for all 0 L, then min(L,L-m) Ry [m] = l=max(0,m) hihm+10 = 2. We simulate Yn with Matlab. As an example of the LTI filter, let hi = [+1 for all 0