Prof. Rich Kozick
ELEC 320, Fall 1997

Homework 22

Date Assigned: Friday, November 14, 1997
Date Due: Wednesday, November 19, 1997

  1. Please begin reading Chapter 7 on the Laplace transform, sections 7.1, 7.2, and 7.3. Also, if you have notes on the Laplace transform from previous courses (MA 212 or EE 209), you might want to find and review those notes.

  2. Problem 5.35 in the text, parts (a) through (e).

  3. Given that signals transmitted over telephone lines have very little frequency content above 4000 Hz, what sampling rate do you think is used in the telephone system?

  4. Consider the "zero-order hold" digital-to-analog converter shown on the back of this page and explained in class. Assume that the analog signal x(t) is band-limited to B Hz, and that the sampling rate Fs = (1/T) > 2B. What should the frequency response of the "reconstruction filter" be so that the output r(t) is identical to the input x(t)? Specify a formula for the frequency response, and also sketch the magnitude and phase of the frequency response.

  5. FFT Question: Please submit by Friday, November 21, and refer to Lab 6.
    You are given a data file sig1.dat that can be downloaded from the Web. This file contains discrete-time data that was obtained by sampling a continuous-time signal at the rate of 60 samples per second. The data can be loaded into Matlab with the command

    load sig1.dat -ascii

    after which a variable named sig1 will be available.

    Suppose it is known that either two or four distinct sine waves are present in the data. How many sine waves do you think are present in the data, two or four? What are their frequencies, in Hertz? Explain your reasoning.

Thank you.