Prof. Rich Kozick
ELEC 320, Fall 1997

## Homework 14

Date Assigned: Monday, September 29, 1997
Date Due: Friday, October 3, 1997

Quiz 2 will be on Friday, October 3. The topics for the quiz include classifying systems (linear and time-invariant), impulse response, and convolution for discrete-time and continuous-time systems. Lab this week will be devoted to exercises in computing the convolution operation.

Please be sure that you make good use of class time, lab time, and office hours this week so that you can successfully complete this assignment by Friday and be prepared for Quiz 2 on Friday.

1. Find the impulse response h[n] of the discrete-time system
y[n] = 0.2 * ( x[n] + x[n-1] + x[n-2] + x[n-3] + x[n-4] )
This system is a simple digital filter. You can listen to a demonstration of sampled music that is filtered by this system by clicking on the "Digital Filter Demo" at
http://www.eg.bucknell.edu/~kozick/elec320/notes.html
What type of filter is this system (low-pass or high-pass)?

2. More practice with impulse response: Problem 3.2 in the text.

3. Discrete-time convolution: Problem 3.4, part (b) (already done on previous assignment), and Problem 3.5, parts (a) and (b). Check your results with the MATLAB command conv.

4. A Java applet that graphically illustrates continuous-time convolution is available at
http://spectrum.ece.jhu.edu/wjr/
with the title "Joy of Convolution". The demonstration appears to be incomplete in that the final result is not plotted, but I think it still has some value in helping to visualize the convolution operation. You should check it out. (Nothing needs to be handed in for this part.)

5. Continuous-time convolution: Problem 3.15 (all parts) and Problem 3.19 (hint for part b: use linearity and time-invariance with your answer from part a).

6. The impulse response for the RC circuit shown below is h(t) = (1/(RC)) exp[-t/(RC)] u(t). (Extra Credit: Try to show this!) Assume that the capacitor is initially uncharged, and that RC = 0.001 seconds. Find the output voltage y(t) when the input voltage x(t) = u(t) - u(t - 0.001) volts.

Thank you.