ELEC 320, Fall 2006
Prof. Rich Kozick

## Homework 14

Date Assigned: Monday, November 27, 2006
Date Due: Monday, December 4, 2006
(Not really - submission of your solutions is optional and will be graded as extra credit. I will post solutions to these problems, and I will try to schedule a review session before the final exam to go over these problems and answer any other questions that you have.)

1. Reading: Please continue to study Section 5.1 on the sampling theorem for class on December 1. You may also want to browse sections 5.2 and 5.3 on the DFT and FFT (we discussed these in Lab 8).

For December 1 and 4, please begin reading Chapter 6 on the Laplace transform. Sections 6.1 and 6.2 describe the forward and inverse Laplace transform operations. You should study these sections carefully, focusing on the unilateral Laplace transform. Please note that Sections B.3-2 and B.5 in the Background chapter are useful. Sections 6.3 and 6.4 describe the application of the Laplace transform to solving differential equations and circuits (ZSR and ZIR!). Since you have done this in MATH 212 and ELEC 225-226, we will mention it only briefly in this course. The concept of the transfer function of an LTIC system, H(s), is very important. Please browse Section 6.5 on block diagrams and Section 6.6 to understand how higher-order systems are designed. You will use these methods extensively next year in ELEC 480 (Control Systems). You can skip Sections 6.7, 6.8, and 6.9.

If you have notes on the Laplace transform from previous courses (MATH 212 and ELEC 225-226), you might want to find and review those notes.

If you would like to read more about topic that began the course, analog filters, please read Sections 7.1 and 7.2 on frequency response and Bode plots. We have already covered the basic material in these sections, and we will not consider all of the details in these sections. Section 7.4 is useful and interesting - it explains filter design by placing poles and zeros in the s-plane. Section 7.5 discusses the Butterworth filter. These sections will provide an introduction to the design of higher-order analog filters (higher than first-order). However, we will not have time to discuss this material in class.

2. Lab Design Project: We will work on your projects on November 27 & 29, and you will present your results on December 4. Please see the labs link on the course web page for more details.

3. The problems on Homework 13 are due on Friday, December 1.

4. Final exam: The final exam for ELEC 320 is scheduled for Monday, December 11 at 8:00 A.M. in room Dana 113.

5. Please solve Problem 5.1-4 in the Lathi text on the zero-order hold digital-to-analog (D/A) conversion system.

6. Answer the following additional question related to the zero-order hold D/A converter. Assume that the analog signal f(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" that is applied to the output of the system in Figure P5.1-4 so that the result is identical to the original analog signal, f(t)? Specify a formula for the frequency response, and also sketch the magnitude and phase of the frequency response.

7. Please check out the following demonstrations at the Johns Hopkins demo page,
http://www.jhu.edu/~signals/
• For the sampling theorem, SampleMania
• For Laplace transform applied to LTI systems, Exploring the s-Plane
Nothing needs to be submitted for this item. Just have fun and learn.

8. Please solve the following problems in the Lathi text for practice with the material in Chapter 6. You will not be responsible for the material in Chapter 7.
Problems 6.2-1 and 6.2-3 (for practice with the forward and inverse L.T.)
Problems 6.3-1(b) and 6.3-5 (for solving differential equations)
Problems 6.4-3 and 6.4-9 (for L.T. applied to circuit analysis)
Problems 6.5-2 and 6.6-1 (for block diagrams and system realization)
Problem 7.1-1 (for frequency response from H(s))
Problem 7.4-1 (for frequency response from pole-zero locations)
Problem 7.5-1 (for Butterworth filter design, but you can use the tables)

Thank you.