# Fourier transform calculation never stops [closed]

I'm trying to calculate a Fourier transform and plot it, however the calculation is running for several hours now. I suspect that there is a mistake in my script. Or am I just not patient enough? Is there any shortcut, like evaluating the FT numerically? When I encounter this problem with Integrate, I usually still get reasonable and quick results using NIntegrate. Is there anything like that for Fourier transforms as well?

beta2 = -7.63;
fs = 39 ;

spectrumdisp[f_, fs_, beta2_, L_] :=
Exp[-I*beta2*f^2*L/2]*Exp[-((f/(2*fs))^2)^3];

Plot[Abs[FourierTransform[spectrumdisp[f, fs, beta2, 1], f, t]], {t, 1, 100}]


However, i'm not sure if the FourierTransform alone works this way at all. Already this command does not finish calculating:

FourierTransform[spectrumdisp[f, fs, beta2, 100], f, t]


I would be very glad if someone could help me with these problems.

## closed as off-topic by Daniel Lichtblau, MarcoB, m_goldberg, Alex Trounev, xzczdApr 7 at 10:21

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• First problem: Replace == by =: beta2 = -7.63; fs = 39;. – Henrik Schumacher Apr 5 at 7:41
• Try in addition to @Henriks comment Plot[Abs[FourierTransform[spectrumdisp[f, fs, beta2, 1], f, t]] // Evaluate, {t, 1, 100}] – Ulrich Neumann Apr 5 at 15:16
• @HenrikSchumacher, thanks, i edited it above. – Mechanix Apr 6 at 17:08
• @UlrichNeumann this makes it actually so much faster. Now, it takes only a few seconds. Can you explain to me, when and how often the fourier transform is evaluated now? – Mechanix Apr 6 at 17:13
• @Mechanix Quite often there is some kind of conflict inside Plot-function with the plot-variable t .  Evaluate forces the evaluation of the plotfunction before plotting. – Ulrich Neumann Apr 7 at 9:31