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.
>
>