Math 4330, Homework 3, 2/5/2014
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Read 4.3.3.C (up to the middle of page 306 Do a web search to learn a little about
complex numbers in Python (2.7). Then do the following:
1. Write a function print_comp_list(zlist) which takes as input a list zlist of complex numbers and prints them out, comma-separated, to three decimal places.
2. Write a function DFT(u) which takes as input a list u of complex numbers, computes
and returns their DFT using Equation (35) from Knuth.
3. Create a list u containing the sequence of complex numbers 0,1,0,-1,0,1,0,-1. Print u,
DFT(u), and DFT(DFT(u)).
4. Roughly how many operations would your DFT function require to compute the Discrete
Fourier Transform of a list of 106 complex numbers? Roughly how many operations
would a Fast Fourier Transform require to do the same?
5. Find at least 4 distinct interesting applications of the DFT/FFT. (You need not describe the applications in detail - one or two sentences about each will suffice)
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Chris Monico, and may not be reproduced in any form without
written permission from the author.
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