# Question: The sum of two independent random sequences with autocorrelation functions is

The sum of two independent random sequences with autocorrelation functions

is input to an LTI filter.

(a) Determine the Wiener smoothing filter. That is, find the impulse response of the filter which produces an output which is an MMSE estimate of S [n].

(b) Find the PSD of the filtered signal plus noise.

(c) Find the input SNR and an estimate of the output SNR. Discuss whether or not the Wiener filter improves the SNR.

is input to an LTI filter.

(a) Determine the Wiener smoothing filter. That is, find the impulse response of the filter which produces an output which is an MMSE estimate of S [n].

(b) Find the PSD of the filtered signal plus noise.

(c) Find the input SNR and an estimate of the output SNR. Discuss whether or not the Wiener filter improves the SNR.

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