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]) -- To reply via email subtract one hundred and four