Suppose that we are given a measurement characterized by y(t) = x(t) + n(t) where x is exponentially correlated Rxx (k) = ( 1/2 ) |k| and n is zero-mean, white noise with variance Rnn = 5. (a)...

Suppose that we are given a measurement characterized by

y(t) = x(t) + n(t)

where x is exponentially correlated Rxx (k) = ( 1/2 )^|k|
and n is zero-mean, white noise with variance Rnn = 5.

(a) Determine the optimal realizable Wiener filter.

(b) Determine the optimal realizable Wiener filter for one-step prediction, that is, x(t + 1|Yt).

(c) Simulate the process and obtain the Wiener solution in both time and frequency domain.