## Laboratory 4 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.

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.

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?

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.

Explain your results, based on the form of the system's step and impulse responses.

4. Please use this lab as an opportunity to learn about Matlab. Describe what you want to do, and we'll help you do it in Matlab.

5. Please submit a lab report for each pair of students explaining your results and answers to the questions. The report can be hand-written, if you would like, and it is due on Friday, October 22, at 9 AM.

Thank you, and have fun!