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

```

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