ELEC 320, Fall 1998
Prof. Rich Kozick

Homework 14

Date Assigned: Friday, October 16, 1998
Date Due: Monday, October 19, 1998

  1. Please read Sections 4.1 and 4.2 on Fourier Series.

  2. Please experiment with the Fourier series demonstrations at
    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).

Thank you.