This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 kth 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 ....
View
Full
Document
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
 Staff

Click to edit the document details