ELEC 320, Fall 2004
Prof. Rich Kozick

## Homework 10

Date Assigned: Wednesday, October 13, 2004
Date Due: Friday, October 15, 2004

1. Please continue to study Chapter 3 in the Lathi text on Fourier series.

2. Please experiment with the Fourier series demonstrations at
http://www.jhu.edu/~signals/ with the title "Fourier Series Approximation".

Under Fourier Series Approximation:
(a) Which signal is easier to approximate, the "Rectangular Pulse" or "Triangle"? That is, if 10 coefficients are used, which signal is better approximated? Please explain why this is the case by observing the shape of the magnitude spectrum at the higher frequencies.
(b) How is the magnitude spectrum of "Noise" different from the other signals? Specifically, what do you notice about the "strength" of the higher frequencies in the magnitude spectrum?

Try the demo that is titled "Listen to Fourier Series". Did you learn anything interesting from this demo?

3. Prove that for a continuous-time system that is linear and time-invariant, the zero-state response (ZSR) of the system to a sinusoidal input is a sine wave with the same frequency as the input wave, but a different amplitude and phase shift. Also, find an expression for the frequency response of the system in terms of the impulse response.

Some hints about how to proceed with this problem: PDF file or HTML file (both files have identical content).

4. Exam 2 will be on Wednesday, October 20.

5. For Lab 4, please submit a 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.