Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2007
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Re: Porting waveforms out of Mathematica and into a D/A converter
  • Next by Date: Re: How to make a loop for this problem!
  • Previous by thread: Re: FourierTransform and removable singularities
  • Next by thread: Re: FourierTransform and removable singularities