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Topic: Discrete Fourier Transform in 2D
Replies: 2   Last Post: May 7, 2011 10:36 PM

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Dave Dodson

Posts: 690
Registered: 12/13/04
Re: Discrete Fourier Transform in 2D
Posted: Apr 16, 2011 12:47 AM
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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 conjugate-symmetric function (see
http://en.wikipedia.org/wiki/Discrete_Fourier_transform#The_real-input_multidimensional_DFT).
The inverse DFT of a complex conjugate-symmetric function is real.

Dave



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