In practice, images always have finite size and are obtained by some
form of sampling of the scene either by a CCD camera or the eye.
For an image array of size 
, the discrete Fourier
transform and its inverse are given by
As in the case of 1-D signals, the transform is periodic in both
. Also the inverse Fourier transform is doubly periodic
in 
, that is to say that the left and right sides of the image
have the same intensity, as do the top and bottom. When this
assumption is not met, the discontinuity introduces some artifacts.
There are several commonly used approaches to this problem. One of
them is to use a window to modulate the border so that it drops to
zero. Another is to extend the image by a border of zeros and yet a
third is to add a mirror image of the last several rows of pixels to
both the directions. Which one is used depends on what the
qualitative nature of the artifacts introduced is like.