A random process x(n) is given as where is an additive white noise sequence wi...

A random process x(n) is given as

where is an additive white noise sequence with variance

(a) Generate N = 1000 samples of x(n) and simulate an adaptive line enhancer of length L = 4. Use the LMS algorithm to adapt the ALE.

(b) Plot the output of the ALE.

(c) Compute the autocorrelation of the sequence x(n).

(d) Determine the theoretical values of the ALE coefficients and compare them with the experimental values.

(e) Compute and plot the frequency response of the linear predictor (ALE).

(f) Compute and plot the frequency response of the prediction-error filter.

(g) Compute and plot the experimental values of the autocorrelation of the output error sequence for 0 ≤ m ≤ 10.

(H) Repeat the experiment for 10 trials, using different noise sequences, and super-impose the frequency response plots on the same graph.

(i) Comment on the result in parts (a) through (h).