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I have an image, which has an inherent mask built into it. The exact shape isn't super important, but it looks something like a circ multiplied by a rect. I would like to calculate the 2D Fourier transform of only the masked region. If I calculate the Fourier transform over the full image it will have spatial frequencies associated with the mask, not the underlying image. Does anyone know how to do this?

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I don't think what you're asking for is possible. If you take the Fourier transform with the existing mask / window function you're going to get the spectral content of the underlying image convolved with the spectral response of the mask due to multiplication in the time domain being equivalent to convolution in the frequency domain.

An alternative is to take the Fourier transform or a subset of the masked image, but this will just result in what is effectively a new mask being applied to the underlying image.

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  • $\begingroup$ hmm yes, this is kind of what I thought. So is there no better solution than just applying some kind of Tukey window on top of my image to suppress the high frequency content due to the edge of the inherent window function? (I'm interested in measuring the amount of high frequency content) $\endgroup$ Jan 25 at 1:18
  • $\begingroup$ @user2551700, I believe so. There may be some more sophisticated windowing possible but I don't do much image processing so I haven't ever investigated it. $\endgroup$ Jan 25 at 1:30

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