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The reason I'm asking is because I need to construct a filter that acts on a 2D surface, which filters each frequency w with the factor tanh(w)/w, disregarding of the direction along the surface. If I can only calculate the Fourier transform of the function just gave, I will get a 2d convolution filter which I can use.

Any idéas of how to approximate the 2D Fourier transform of the function? Thanks in advance.