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/999d7a07-cff7-4a09-9aa0-17fa6b55c2b4.png)
![](https://test.transtutors.com/qimg/159000f7-7443-4116-b445-382126af86d1.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/ff19e059-18cb-480a-9cc2-318931d116aa.png)
c) Find an expression for the mean square error ![](https://test.transtutors.com/qimg/5b3f760a-243a-4926-9564-8935a69ec5d7.png)