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
    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

    load sig1.dat -ascii

    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.

    Explain your reasoning.

  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.

Thank you.