Question

Let Xn, -inf to +inf be a discrete-time zero-mean white noise process, i.e., μx[n] = 0, Rx[n] =δ[n]. The process is filtered using an LTI system with impulse response

h[n] =αδ[n] + βδ[n−1].

Find α and β such that the output process Yn has autocorrelation function Ry[n] =δ[n+1] + 2δ[n] +δ[n−1].

5) (3 points) Let Xn, -o0 K n oo, be a discrete-time zero-mean white noise process, i.e, ,1z[n]-(), Rx [n] S[n]. The process is filtered using an LTI system with impulse response Find α and β such that the output process Yn has autocorrelation function RY[n] 1] + 201n] + δ[n-1]. S[n+

Answer 1

Solution Given that Rx [n] = s[n] We know that ,from the properties of Autocorrelation tunction output spectral-r1nput spectral [[H Denaity ensit The Fouries trans form of Audocorre ta tion Punction is energy signal (or) po cae gignal DTFT x te DTFT

Nlow apply the biscrete time fourie tron orm JW 2. Jh J W Now A pplying the DTFT 2.

2. Substitiute the values Now Composte both si des substitute β-| 2 ence, the Value of dst, and