h06-4 - actual function Consider the fourier basis e inx...

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CIS6930/4930 Intro to Computational Neuroscience Spring 2006 Home Work Assignment 4: Due Wednesday 03/22/05 before class 1. (50 pts) Consider the following function over the range [0 , 1] f ( x ) = - 2 × x if x [0 , 1 3 ] f ( x ) = 1 if x ( 1 3 , 2 3 ) f ( x ) = 0 if x [ 2 3 , 1] Note that the function is such that Z 1 0 f ( x ) dx = 0 First translate and scale uniformly the domain of the fuction so that it now lies on [ - π, + π ] . All future references to f ( x ) is this scaled and translated version. Your goal will be to find an approximation of this function as a fourier series, and show the graphs of successive approximations overlayed on the
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Unformatted text preview: actual function. Consider the fourier basis e inx for n =-N, . .., + N , and the corresponding sum + N X n =-N c n e inx Calculate the values of c n by numerically approximating the integral Z + π-π f ( x ) e-inx dx , that is, by dividing the range [-π, + π ] , into small intervals and approximating the integral as a sum. Show graphs of how well f ( x ) is approximated by overlaying the series over f ( x ) for various values of N (for example, N = 5 , 10 , 20 , 50 ). 1...
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