Re: FoourierTransform of a function defined in sections

• To: mathgroup at smc.vnet.net
• Subject: [mg70217] Re: FoourierTransform of a function defined in sections
• From: Bill Rowe <readnewsciv at sbcglobal.net>
• Date: Sat, 7 Oct 2006 07:08:54 -0400 (EDT)

```On 10/6/06 at 1:59 AM, e.schlemm at hotmail.de (Eckhard Schlemm) wrote:

>I want Mathematica to calculate the FourierTransform of a function
>which is defined by Sin[x]^2 for Abs[x]<PI and zero else. I tried
>and defined the function g as follows:

>g[x_]:=If[Abs[x]>PI,0,Sin[x]^2];

>That works fine. But if I have mathematica try to determine the
>FourierTransform by

>FourierTransform[g[x],x,p]

>I always get the error that the recursion limit and the iteration
>limit were exceeded...

Try defining g in terms of UnitStep, i.e.,

In[10]:=
g=Sin[x^2](UnitStep[x+Ï?]-UnitStep[x-Ï?]);
FourierTransform[g,x,w]

Out[11]=
(1/2)*(Cos[w^2/4]*(FresnelS[(2*Pi - w)/Sqrt[2*Pi]] +
FresnelS[(w + 2*Pi)/Sqrt[2*Pi]]) -
(FresnelC[(2*Pi - w)/Sqrt[2*Pi]] + FresnelC[(w + 2*Pi)/Sqrt[2*Pi]])*
Sin[w^2/4])
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