EE 329
Prof. Rich Kozick
Spring, 1997

EE 329: Homework Assignment #3

Date Assigned: Monday, February 10, 1997
Date Due: February 12 and 14, 1997

  1. Continue working on your FFT program as described on the Lab 3 handout. Submit your Matlab programs by Friday, February 14.
  2. Also for Friday, explain why the computational complexity of the FFT algorithm is tex2html_wrap_inline46 when tex2html_wrap_inline48 is a power of 2. We showed in class that each butterfly requires 1 complex multiply and 2 complex additions. You should explain why tex2html_wrap_inline46 butterflies are needed.
  3. Please work on the following problem for Wednesday, February 12. Bring your plots, ideas, and questions to class on Wednesday for discussion. Then I will ask you to summarize your results and submit them on Friday.

    1. Consider an analog signal that is a rectangular pulse described by x(t) = 1 for tex2html_wrap_inline54 and x(t) = 0 otherwise. Convince yourself that the Fourier transform of x(t) has magnitude
      Sketch tex2html_wrap_inline60 versus frequency f in hertz, and plot using Matlab over the range tex2html_wrap_inline64 Hz.
    2. Use the FFT to compute and plot the magnitude spectrum of x(t). Note that in order to use the FFT, the analog signal x(t) needs to be sampled at some rate tex2html_wrap_inline70 and with some number of sampling points N. What are the considerations in choosing tex2html_wrap_inline70 and N? Try various values for tex2html_wrap_inline70 and N, and plot the FFT magnitude spectra obtained with Matlab. Try to explain the results that you are seeing. Be sure to label the FFT spectra with hertz along the horizontal axis. Can you obtain a spectrum with the FFT that is close to the analytical result in part (a)?

Kozick Rich
Sun Feb 9 18:02:20 EST 1997