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. > >