EE 547 Project #2 Fall 1999

Difference Equations and Impulse Responses

This project will help you to become more familiar with difference equations by exploring their characteristics in both the time and frequency domains.

1. Let . This difference equation can be implemented using the filter command. Find the vectors a and b that represent the difference equation above for the filter command.
2. Calculate analytically for the difference equation above. Hint: You may find the roots function useful.
3. Create an impulse of length 128. Find the first 128 points of the impulse response using filter, and plot the result with stem.
4. Create a pulse of width 7 and zeropadded to a total length of 128. Find the response of the system to this input using conv by convolving with the impulse response and with filter by filtering with the difference equation. Explain any differences you observe.
5. Find an expression for the frequency response of the system described by the difference equation given.
6. Use the command freqz to plot the magnitude and phase response of the system. Is this system a highpass, a lowpass, or a bandpass filter?
7. Create two signals and , both of length 128. Filter both signals with the filter defined in Step 1. Explain what you observe in terms of the frequency response of the system.

Write a short report describing your findings. The report should contain a concise description of your results. Include listings of your function. Be sure to answer all questions. Do not include more than six plots in your report. You are not expected to include in the report all plots which you were required to do; instead, you should summarize in your report the salient features of the unincluded plots.

For further help:

• Matlab Primer

• Matlab Online Reference

• About this document ...