Fourier and InverseFourier

*To*: mathgroup at smc.vnet.net*Subject*: [mg75396] Fourier and InverseFourier*From*: rob <josh2499 at hotmail.com>*Date*: Sat, 28 Apr 2007 05:56:25 -0400 (EDT)

I kind person on this ng (Gulliet) recently contributed a convolution scheme which works nicely to plot x2 below: conv[f1_, f2_] := Module[{u}, Evaluate[Integrate[f1[u] f2[# - u], {u, 0, #}]] &] x2[t_] := convolve[Sin[t], Exp[-t]][t] Plot[x2[t], {t, 0, 15}, PlotRange -> All] Wondering if I could achieve the same thing in the freq. domain, I tried what I thought should give the same result in x3: fs = FourierTransform[Sin[t], t, w] fe = FourierTransform[Exp[-t], t, w] x3[t_] := InverseFourierTransform[fs*fe, w, t] Plot[x3[t], {t, 0, 15}, PlotRange -> All] I find this does not work, getting this err message and Mathematica (v.5.1) didn't stop in over 30 minutes. NIntegrate::ploss: Numerical integration stopping due to loss of precision. Achieved neither the requested PrecisionGoal nor AccuracyGoal; suspect one of the following: highly oscillatory integrand or the true value of the integral is 0. If your integrand is oscillatory on a (semi-)infinite interval try using the option Method->Oscillatory in NIntegrate. Since I'm using the internal integrals of InverseFourierTransform I don't know how to try the suggestion of Method->Oscillatory as the message suggests. I changed the Sin[t] to t and the process gave no err messages and finished in just a few minutes. The plot had axes but nothing on it. Can someone give me any hints as what might work?