I'm trying to obtain the fourier transform from overlapping blocks of an image, say blocks of 32x32 pixels with overlap of 16 pixels. I do not want to calculate, or at least I want to avoid to calculate, the FT of each block separately. My question is: Is there some "simple" way to get the Fourier Transform of a sub-window of an image from the Fourier Transform of the whole image? For example, to obtain the FT of the image once, and by some "simple" operation to obtain the FT of a sub-image from the first FT. A friend of mine show me how can be done in one dimensional signals, say audio or radio. But he does not know about images (2D signals?), only showed me an approximation. Can someone explain me or show me some reference on how it can be done, if exists at all any method? I could not find any. My Google-fu has been helpless.
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