For the digital filter of Problem 11.2.6, generate 100 sample paths Y0,..., Y500 assuming the Xi are iid Gaussian (0, 1) random variables and Y(0) = 0. Estimate the expected value and variance of Yn for n = 5, n = 50 and n = 500.
Problem 11.2.6
The input ..., X-1, X0, X1,... and output ..., Y-1, Y0, Y1,... of a digital filter obey
![](https://test.transtutors.com/qimg/1b48183f-e6ae-4962-b248-80d2e942ab84.png)
Let the inputs be a sequence of iid random variables with E[Xi] = µXi = 0 and Var[Xi] = σ2. Find the following properties of the output sequence: E[Yi], Var[Yi], Cov[Yi+1, Yi], and ρYi+1,Yi.