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 (137.48 KiB) Viewed 36 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. ii) Write a Matlab function called radix2ifft.m which implements the radix 2 algorithm of the inverse fast Fourier transform. You can either modify the Matlab function radix2fft.m (which implements the Fourier transform using a recursive algorithm), or come up with your own version. The function radix2fft.m can be downloaded from the course Moodle page in the folder Lecture 06. An explanation of the idea of this program is in the handwritten notes Lecture06notes2.pdf, also in the folder Lecture 06. This was discussed at the beginning of the lecture in Week 7 . You can only use +,−,∗,l,exp, for, while and so on, but not fft, if ft or other built-in functions from Matlab. The input is a row vector of length 2m for some non-negative integer m. The function should return an error message if the length of the input vector is not of length 2m for some non-negative integer m. Function 8