# 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.

**View Solution:**## Answer to relevant Questions

Consider the experiment of tossing a six sided die as described. Suppose the die is loaded and as such we assign the following probabilities to each of the six outcomes: Is this assignment consistent with the three axioms of ...The PSD of a narrowband Gaussian noise process, N (t), is as shown in the accompanying figure. (a) Find and sketch the PSD of the I and Q components of the narrowband noise process. (b) Find and sketch the cross- spectral ...If the input to a linear filter is a random telegraph process with c zero- crossings per second and amplitude A, determine the output PSD. The filter impulse response is h (t) = bexp(– at) u ( t). Prove that the importance sampling (IS) estimator of Equation (12.26) is unbiased. That is, show that Suppose a pseudorandom sequence is constructed using the power residue method. If q = 11, find a value of that leads to a sequence with maximum possible period. X k = ax k – 1 mod q, k = 1, 2, 3… Find the period and the ...Post your question