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MathGroup Archive 2007

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Re: FourierTransform and removable singularities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75310] Re: FourierTransform and removable singularities
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 25 Apr 2007 05:28:35 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <f0kbmk$qvt$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

Limit[FourierTransform[DiracDelta[t - a]*(Sin[
       t]/t), t, w] // FullSimplify, a -> 0]

Regards
   Jens

Roman wrote:
> It seems to me that Mathematica 5.2 is not careful enough when doing
> Fourier transforms of functions with delta functions at removable
> singularities: if you call
> 
>     FourierTransform[DiracDelta[t], t, w]
> 
> you get the right answer,
> 
>     1/Sqrt[2*Pi]
> 
> But if you call something of the sort of
> 
>     FourierTransform[DiracDelta[t]*(Sin[t]/t), t, w]
> 
> which has a removable singularity at the point where the Dirac delta
> function acts, the answer is zero, which is wrong.
> 
> Does anyone know how to resolve this by reformulating the problem? (a
> workaround)
> 
> Cheers!
> Roman.
> 
> 


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