ELEC 320, Fall 2004
Prof. Rich Kozick

Homework 16

Date Assigned: Wednesday, November 17, 2004
Date Due: Monday, November 29, 2004

1. Exam 3 will be on Friday, November 19, 2004. The exam topics are the Fourier series and the Fourier transform. I will provide you with the formulas for the Fourier series and tables of Fourier transform pairs and properties.

2. Reading: Please continue to study Section 5.1 on the sampling theorem. You may also want to browse sections 5.2 and 5.3 on the DFT and FFT (we discussed these in Lab 7).

For the week of November 29, please begin reading Chapter 6 on the Laplace transform. Sections 6.1 and 6.2 describe the forward and inverse Laplace transform operations. 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.

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. This might make some enjoyable reading over Thanksgiving break.

3. Lab Design Project: We will work on your projects on November 22-23 and 29-30, and then you will present your results on December 6-7. Please see the labs link on the course web page for more details.

4. Please answer the following question related to the fast Fourier transform (FFT). Refer to Lab 7 for notes on how to perform the FFT with MATLAB.

You are given a data file sig1.dat that can be downloaded from the Web version of this assignment at
http://www.eg.bucknell.edu/~kozick/elec32004/hw16.html
The file contains discrete-time data that was obtained by sampling a continuous-time signal at the rate of 300 samples per second. The data can be loaded into MATLAB with the command

after which a variable named sig1 will be available. (The MATLAB command whos gives you a listing of all variables defined in the MATLAB workspace.)

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?
• Is there a difference in amplitude among the sine wave components? If so, which frequency component(s) have the largest amplitude?