ELEC 320, Fall 1998
Prof. Rich Kozick

## Homework 19

Date Assigned: Wednesday, November 18, 1998
Date Due: Monday, November 23, 1998

1. Quiz 5 will be take-home. It will be distributed on Monday, November 30 and will be due on Wednesday, December 2.

2. Reading on sampling theorem: pages 186-189 and 240-244.

3. Given that signals transmitted over telephone lines have very little frequency content above 3400 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 samples/sec. What should be the frequency response of the "reconstruction filter" 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. Reading for week of November 30: Please begin reading Chapter 7 on the Laplace transform. Sections 7.1 - 7.3 describe the forward and inverse Laplace transform operations. Section 7.4 describes the application of the Laplace transform to solving differential equations. Since you have done this in MATH 212, we will mention it only briefly in this course. The concept of the transfer function in Section 7.5 is very important.

If you have notes on the Laplace transform from previous courses (MATH 212 and/or ELEC 220), you might want to find and review those notes.

6. If you want to get ahead, I will ask you to do the following inverse Laplace transform problems after Thanksgiving:

Problem 7.9, parts a, b, c, d, f, and g.

For each problem, perform the partial fraction expansion analytically, and then check your results using MATLAB.

Thank you.