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Unformatted text preview: ECE130B Jan. 26, 2010 Home work 4 Due date : Monday, February 1, 2010, by 5p.m. at the home work box. Exercise 1. Given a length N signal x [ n ] , find the number of arithmetic operations that the algorithm you implemented in Home Work 3 , Exercise 4 , requires. Note : complex exponenti- aition, multiplication, addition, division, subtraction, cosine and sine, can all be computed as a single arithmetic operation for this exercise. Exercise 2. Report the time taken by your code from Home Work 3 , Exercise 4 , for signals of length 2 12 , 2 13 and 2 14 . Make sure you only time the code that computes the Fourier series coef- ficients. FFT . The F ast F ourier T ransform is an algorithm for computing the discrete Fourier series coefficients rapidly. We briefly describe one version when the length N of the signal is an exact power of 2 ; that is N = 2 M for some integer M . Let x [ n ] be the given signal for n = 0 , , N- 1 . The k-th Fourier series coefficient of this signal is given by the formula: a k = 1 2 M summationdisplay n =0 2 M- 1 x [ n ] exp parenleftbigg- 2 j k n 2 M parenrightbigg ....
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This note was uploaded on 04/06/2010 for the course ECE 130b taught by Professor Staff during the Winter '08 term at UCSB.
- Winter '08