What is Discrete Fourier Transform (DFT)? Find DFT of the function:
The discrete Fourier transform (DFT) represents a finite-length discrete signal by a finite set of complex exponentials. For a 2-D M×N array f(x,y) with 0≤x≤M−1 and 0≤y≤N−1, its 2-D DFT is $$ F(k,\ell)=\sum_{x=0}^{M-1}\sum_{y=0}^{N-1} f(x,y)\,e^{-j2\pi\left(\frac{kx}{M}+\frac{\ell y}{N}\right)},\qquad k=0,\dots,M-1,\;\ell=0,\dots,N-1. $$ The inverse is $$ f(x,y)=\frac{1}{MN}\sum_{k=0}^{M-1}\sum_{\ell=0}^{N-1} F(k,\ell)\,e^{+j2\pi\left(\frac{kx}{M}+\frac{\ell y}{N}\right)}. ___ ______ __________ ___ ____ _______ __________.
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What is Discrete Fourier Transform (DFT)? Find DFT of the function: