Here you are going to write a function that uses the in-built functions pwelch and cpsd, and you are going to use the results to examine H1 and H2 estimates of H, and the coherence function.  You will use your program to examine effects of window type on the results and the effects of different window sizes.

This is similar to the feedback example we did in class, but the noise comes into the system in the feedback loop, rather than corrupting the output of H(f).

Here you are going to write your own segment averaging code.

This is mostly from your class notes.

This is using the MATLAB program that does the optimal design.

Don’t forget to normalize frequencies by dividing by fs/2.

You may have to “play” a bit to get a good filter design.

By the way when you are testing filters by putting signals through them,  make sure the input signal is long enough so you have some steady state behavior.  Note also that the length of the output will be longer than the input because of the convolution.   Make sure you align the time axis properly.  It would be nice to plot the idea result on the same graph as the output of the filter.

See Lecture 22 Notes for this FIR Design Approach

See Lecture 21 notes starting at page 6 for a recap on this method.

Please write your own programs for this problem, rather than using canned matlab programs.  Take care on your calculation of how many poles or zeros are at the origin.

Post your General Questions and Exam-Specific Questions Here

Homework Set 4 Problem 5

It will be very important to get the complex conjugate symmetry about fsnew/2 correct.   An indication that you didn’t is getting a significant imaginary component when you inverse transform to get the upsampled signal.  If the symmetries in the frequency domain for a real signal in the time domain are correct, the imaginary part should be tiny (due to rounding errors) when compared with the real part, and then you can just set it to the real part.