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Re: Discrete Fourier Transform in 2D
Posted:
Apr 16, 2011 12:47 AM


On Apr 15, 10:36 pm, "Will C." <will53...@gmail.com> wrote: > Hi, > > I am trying to creating an algorithm to compute the fourier transform > of a 2D array for use in a program which compares the performance of > image filters in the spatial vs frequency domain. > > Part of the transform equation contains the term: exp(j * 2 * pi * > ((u * x) / M + (v * y) /N)) > > My question is, how can I get a real solution from this? Since u, v, > x, and y are indexes they are positive, and since M and N are the > dimensions of the original array they are also positive. > > This leaves something like: exp(j * c), where c is a positive > constant which is calculated from the above givens. How can I ever > get a real solution from this?
Why do you expect to get a real solution? Typically, the DFT of a real function is a complex conjugatesymmetric function (see http://en.wikipedia.org/wiki/Discrete_Fourier_transform#The_realinput_multidimensional_DFT). The inverse DFT of a complex conjugatesymmetric function is real.
Dave



