ELEC 320, Fall 2006
Profs. Wismer & Kozick

## Laboratory 5 Numerical Impulse Response and Convolution

The main objective in lab this week is to obtain an estimate of the unit impulse response of a LTI continuous-time system from discrete-time samples of its unit step response. Then you will use Matlab to numerically evaluate the effect of this system on some communication pulses.

Please use this lab as an opportunity to learn about Matlab. Begin by defining the algorithm that you want to implement, and then we'll help you find the proper syntax and commands to do it in Matlab.

This file contains discrete-time samples of the unit step response of a linear, time-invariant, continuous-time system. The variable t contains the time instants, and the variable s contains the step response amplitude. (The Matlab command whos lists the variables in the workspace.)

2. Find an approximation to the unit impulse response of the system, h(t). Explain your reasoning, and compute the samples of your impulse response estimate.

What type of system does this resemble? (It may be useful to plot the impulse response.)

3. Use Matlab to estimate the output of this system to sequences of bipolar, rectangular pulses with the following pulse durations, T (and corresponding pulse rate 1/T pulses/sec). You should make a sequence of at least 10 pulses with amplitudes of +1 or -1.
• T = 0.1 seconds
• T = 0.01 seconds
• T = 0.001 seconds

Your objective is to approximate the convolution integral using the discrete-time samples. You may want to use the conv command in Matlab.

For which value(s) of T are the pulses "passed" by the system with little distortion? For which value(s) of T are the pulses severely "smeared" so that bit errors would be likely? Explain your results quantitatively based on the value of T and the form of the system's step and impulse responses.

4. Please submit a lab report for each pair of students that includes your Matlab program and explains your results and answers to the questions. The report can be hand-written, if you would like, and it is due by the end of your lab period on October 9 or 11.

Thank you and enjoy.