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.

- 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)?
- More practice with impulse response:
**Problem 3.2** in the text.
- 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`.
- 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.)
- 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).
- 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.