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