image processing – Reciprocal Coordinates in discrete 2D Fourier


Is there a way to obtain the transformation of coordinates along with the Fourier transformation of a discrete data set?

Say I have some pixelwise information

dat = RandomReal[{0, 1}, {21, 21}];

And I know that this information maps to an area of -8 m to 8 m in the real world.

coords = Table[Table[{x, y}, {x, -8, 8, 8/10}], {y, -8, 8, 8/10}];

Is there a way to use the Fourier Transformation and also obtain the reciprocal coordinates in [1/m]?

{fft, fftCoords} = Fourier[dat, PleaseAlsoConsiderThatEachPixelHasACoordinate -> coords]

I hope this brings my question across.

It seems kind of natural to have such functionality somewhere to ensure that the reciprocal coordinates are in line with the way the Fourier transformation is done. But somehow I couldn’t find it.

PS: Also there is no tag “fourier” or “fourier-transformation” as if no one ever has a question on these fundamental matters and the tag-finding algorithm does not seem to find a tag that is somewhere close to this. I cant create new tags, because I don’t have the reputation. Can someone please create some tag in this direction?