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hw4-2

# hw4-2 - ECE130B Jan 26 2010 Home work 4 Due date Monday...

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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 πj k n 2 M parenrightbigg .

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hw4-2 - ECE130B Jan 26 2010 Home work 4 Due date Monday...

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