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[✓] Solve this Infinite integral (see FF1 below)?

Posted 11 months ago
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Hi,

Are there any tips to help the solving and plotting for FF1 go somewhat faster ? (I think the plotting is the real issue) I am indeed using a decent Laptop....but the solving and plotting may take more than 20 min +

Regards,

John

ClearAll["Global`*"]
f[t_] = Exp[- t^2]
Plot[f[t], {t, -10, 10}, PlotRange -> All]
acor[\[Tau]_] = 2*Integrate[f[t]*f[t + \[Tau]], {t, 0., Infinity}]
Plot[acor[\[Tau]], {\[Tau], 0., 10.}, PlotRange -> All]
eq[t_] = acor[t]*Exp[-2. Pi  I \[Omega] t]
FF1 = Integrate[eq[t], {t, 0, Infinity}]
Plot[Abs[FF1], {\[Omega], 0, 100}]

John,

The problem is that MMA can't integrate that function. Do it Numerically:

Plot[Abs[NIntegrate[eq[t], {t, 0, 20}]], {\[Omega], 0, 100}]

I took Integrated it out to t=20 because I think it practically vanishes by 20 but you should check this to make sure.

Regards,

Neil

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