fourier transform question (math based)

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tx213
tx213 2014-2-7
回答： Image Analyst 2014-2-8
Hello all,
I am trying to take Fourier Transform of a function and I would love some pointers on how to best approach it.
My function is a function of (r,phi) and it is a piecewise function where:
f(r,phi) = 0 , r < r_inner f(r,phi) = cos(phi).^2 + (-0.5)*sin(phi).^2 , r_inner <= r <= r_outter f(r,phi) = 0 , r > r_outter
I've attached a figure here. Can I take the FT of the pieces individually and then sum? My research tells me this is OK. Since my function is in polar coordinates, I should take the FT in polar coordinates; is there an efficient (clever) way to go about this given the the nature of the function, perhaps that it is symmetric?
Any suggestions/insight would be really appreciated. Thanks in advance!

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Image Analyst
Image Analyst 2014-2-8
Just pass the image into fft2().

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