Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

I've been using this site for a while now, but this is going to be my first post. I want to pick your brains to get some insight on this problem I'm tackling.

I'm trying to take a Fourier Transform of a function. My function is a function of (r,phi) and it is a piecewise function where:

f(r,θ) = 0 , r < r_inner

f(r,θ) = cos(θ)^2 + (-0.5)*sin(θ)^2 , r_inner ≤r ≤ r_outter

f(r,θ) = 0 , r > r_outter

I've attached a figure here. Can I take the FT of the pieces individually and then sum? My knowledge so far 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 every n*pi ?

Any suggestions/insight would be really appreciated. Thanks in advance!

T

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# Fourier transform of an annulus

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