My guess is that you can't perform any calculations relevant for an
influence function in the Fourier domain and even if you could it
wouldn't improve performance. But please elaborate if you think I'm
wrong.
Well, the point is that convolutions in the spatial domain are
multiplications in the Fourier domain. Multiplications are of course
faster. The question is how much time extra the FFT /IFFT transforms
take. I'm pretty sure others have already tested this, so I was hoping
somebody would remember the timing details.