Say I have an equation for a low pass image filter that is applied in Fourier space  ( exp(-f) ) . How would I go about determining what this filter would look like in pixel space? Is there some way to come up with a sample pattern using a discrete inverse fourier transform?

I am not sure what the notation "exp(-f)" means, but if you have a filter in frequency space that consists of scaling frequencies by some factor, that corresponds to a convolution in pixel space. If you want to know what that convolution is, you can take the Fourier transform of a single pixel, apply the filter and take the inverse Fourier transform of the result.

Thanks a lot! This is exactly what I was looking for.

On 11/20/2017 at 8:48 PM, alvaro said:

If you want to know what that convolution is, you can take the Fourier transform of a single pixel, apply the filter and take the inverse Fourier transform of the result.

In more standard language, the spatial domain impulse response of the filter is the inverse Fourier transform of the frequency domain function you multiply the transformed signal by. Whatever variation of Fourier transform you are using, it should be computed exactly like the inverse Fourier transform of filtered signals.

How are you dealing with periodic inputs and outputs? Are windowing functions involved?