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What are $f$ and $g$? Are they arrays of values that you are accessing, or are they functions that are evaluated at each call (and if so, how computationally difficult are they to compute)? I don't really work with Mathematica, but I can give some general computational guidelines that you can implement. Right now, you are computing $$\sum_{i,j,k,l} ... 3 There are different definitions of the Fourier Transform. The confusion comes from Mathematica and your reference using different definitions for the Fourier Transform. They are equivalent up to a constant. Most people, and Mathematica use the definition:$$F[f](\omega)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty f(x)e^{-ix\omega}dx.$$Others use the ... 18 Different definitions Note that Mathematica and your link use different definitions of the Fourier transform. Mathematica uses (you can see this under "Details and Options" in the documentation):$$\frac{1}{\sqrt{2\pi}} \int_{- \infty}^\infty f(t) e^{j \omega t} dt$$and your link uses:$$\int_{-\infty}^\infty f(t) e^{-j \omega t} dt so the transforms ...