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I have a very basic image processing question for which I have not been able to find an answer so far:

On several occasions I have encountered descriptions of image filters given in the frequency domain as functions of horizontal and vertical frequency. For example something like $H(m, n) = exp(-\pi^2 r^2 (m^2 + n^2))$ where $r$ is a constant and $m$ and $n$ are horizontal and vertical spatial frequency respectively.

Now what I' unsure about is how I would go from such a formula to a filter mask that I can apply to an image by multiplying it with the images frequency domain representation. Say I want the filter mask to have the same size as the original image, which pixel positions in the mask correspond to which spatial frequency values in that case?

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