# Question: Suppose we observe a random process Z t without any

Suppose we observe a random process Z (t) (without any noise) over a time interval (–∞, t. Based on this observation, we wish to predict the value of the same random process at time t + to. That is, we desire to design a filter with impulse response, h (t), whose output will be an estimate of Z (t + to):

(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 RZZ (t) = exp (– |τ|).

(c) Find an expression for the mean square error E [Ɛ2 (t)] = E (Z (t + to) – Y (t)) 2].

(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 RZZ (t) = exp (– |τ|).

(c) Find an expression for the mean square error E [Ɛ2 (t)] = E (Z (t + to) – Y (t)) 2].

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