Re: FourierTransform and removable singularities

*To*: mathgroup at smc.vnet.net*Subject*: [mg75368] Re: FourierTransform and removable singularities*From*: Peter Pein <petsie at dordos.net>*Date*: Fri, 27 Apr 2007 05:20:15 -0400 (EDT)*References*: <f0kbmk$qvt$1@smc.vnet.net> <f0pk9v$1t0$1@smc.vnet.net>

David W.Cantrell schrieb: ... > Perhaps the best way to handle you problem would be to have the sine > cardinal function > > | { 1 if x = 0, > | sinc(x) = { > | { sin(x)/x otherwise > > implemented in Mathematica. But defining that function yourself, it does > not work as desired with FourierTransform. > > David W. Cantrell > Hi David, sorry, I did not believe this. And indeed: In[1]:= Off[General::spell]; Sinc[t_] := Piecewise[{{1, t == 0}}, Sin[t]/t] In[3]:= FourierTransform[DiracDelta[t]*Sinc[t], t, w] Out[3]= 1/Sqrt[2*Pi] In[4]:= TrigToExp[FourierTransform[ DiracDelta[t - b] * Sinc[omega*(t - b)], t, w]] Out[4]= E^(I*b*w)/Sqrt[2*Pi] In[5]:= $Version Out[5]= "5.2 for Linux x86 (64 bit) (June 20, 2005)" Why isn't this the wanted result? Or did you have other (more complicated) FourierTransform[]s in mind? Regards, Peter