Suppose we observe a random process
(without any noise) over a time interval Based on this observation, we wish to predict the value of the same random process at time
That is, we desire to design a filter with impulse response,
, whose output will be an estimate of ![](https://test.transtutors.com/qimg/50c1e730-57f8-4860-b55b-be6687423b72.png)
![](https://test.transtutors.com/qimg/a1cacd10-173b-42c4-b85f-6770c2a7b791.png)
(a) Find the Wiener-Hopf equation for the optimum (in the minimum mean square error (MMSE) sense) filter.
(b) Find the form of the Wiener filter if ![](https://test.transtutors.com/qimg/d7fbcff9-664e-4f10-895e-49c18c7ac51c.png)
c) Find an expression for the mean square error ![](https://test.transtutors.com/qimg/217e65b9-559c-4a6d-8672-5d679da5dd7c.png)