Motivation: In the following question we implement the fast Fourier transform. The fast Fourier transform has led to hug

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Motivation In The Following Question We Implement The Fast Fourier Transform The Fast Fourier Transform Has Led To Hug 1 (103.32 KiB) Viewed 54 times

Motivation: In the following question we implement the fast Fourier transform. The fast Fourier transform has led to huge advances in many areas of science, engineering and computational finance. In answering the question below you should get a better understanding of the underlying idea of the fast Fourier transform, which may be useful since similar ideas can be employed in many applications. c) For data points x0​,x1​,…,xN−1​∈R, the Fourier transform is given by yk​=n=0∑N−1​xn​e−2πikn/N,k=0,1,…,N−1 The inverse Fourier transform is given by xn​=N1​k=0∑N−1​yk​e2πikn/N,n=0,1,…,N−1. i) Write a Matlab function called naiveifft.m which computes the inverse Fourier transform (2) using a straight forward algorithm (using only +,−,∗,l, exp, for, while and so on, but not fft, ifft or other built-in functions from Matlab). The input is a row vector of length N and the output should also be a row vector of the same length. Note: If you define a vector in Matlab say y=[0,1], then y(1)=0 and y(1)=1. If you type y(0) you will get an error message. In other words, vectors are automatically enumerated such that the first element has index 1 , the second has index 2 and so on; In the formula above, the index runs from 0 to N−1 Function 8 \begin{tabular}{|l|l} 1 & function x= naiveifft (y) \\ 2 & % \\ 3 & % compute the inverse Fourier \\ 4 & end \end{tabular} \% compute the inverse Fourier transform