Exercise 3

Assigned: 03/22/12 Due: 03/27/12
Use the data in the table in Problem 6-4.1 in the book to do the following exercises:
  1. Find the sample mean using the MATLAB function mean.

  2. Calculate the estimated autocorrelation function \(\hat{R}(0.01n)\) for \(n = 0,\ldots,20\) using Eq. 6-15, and plot with appropriate index values along the x-axis. You can use the MATLAB function xcorr if it is called with the appropriate options so that it corresponds to Eq. 6-15. You may want to test that you have the correct calling options by hand-calculating a 3-point sequence where you can easily verify and compare the output to your hand calculations. Also, you must think carefully about how to define the index values, since MATLAB does not keep up with the x-coordinate for you.

  3. Calculate the estimated autocorrelation function \(\hat{R}(0.01n)\) for \(n = 0,\ldots,20\) using Eq. 6-16, and plot with appropriate index values along the x-axis. You can use the MATLAB function xcorr if it is called with the appropriate options so that it corresponds to Eq. 6-16.

  4. Explain why the values in #2 vary so much for large \(n\) compared to the same values of \(n\) in #3. Are these values in #2 a reliable indicator of the actual autocorrelation? Why or why not?
Please include all your code. Make your plots no more than 1/4-page high. Please make your write-up as concise as possible while answering all questions.

NOTE: All out-of-class work is to be done independently. Sharing of programming tips and discussing general concepts is ok. Collaborating on experiments or code-writing is not. Any such collaboration on these assignments will be considered an act of academic dishonesty and will be treated accordingly.