Create a MATLAB Model 1) Create a sample function of a random process using the MATLAB function randn.
2) Estimate the autocorrelation of that function using the MATLAB function xcorr. xcorr creates an array that is approximately twice as long as the input array, with the approximation to the true statistical autocorrelation becoming less good near the ends of the output array. Therefore, we will only use the samples near the center of the output array for our estimates of the autocorrelation. Expand the skeleton m-file to perform the following tasks.
3) Plot the (truncated) output of xcorr. This is an estimate of the statistical autocorrelation,.
4) Repeat step 1 through 3 many (e. g., 500 to 5000, more if your computer can do it) times. Each step will create a new sample function of the random process, and a new estimate of the autocorrelation. Because the length of the sample function is not infinite, the estimates themselves will show some variation. This should be obvious from the plots. Store each new sample function and each new autocorrelation in a new row in their respective arrays.
5) Remembering that the true autocorrelation is a statistical average, compute the mean values of the sample functions and the mean values of the autocorrelation functions by averaging down the columns. Plot the results.
6) Discuss each of the plots. Tell me what it represents, why that is important, and why the results might not be what the theory predicts. The more specific your comments, the better.