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How to make the numerical Fourier transform match up exactly with the analytical one? I'll just work a 1-dimensional example here, but it should apply in 2D as well. We take a Gaussian pulse whose phase is zero at time zero, and it should have a completely real and positive Fourier transformation pulse[t_] := Exp[-t^2/ (2 σ^2)] Exp[-I ω0 t]; pulseω = ...

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