Re: FourierTransform and removable singularities

*To*: mathgroup at smc.vnet.net*Subject*: [mg75404] Re: FourierTransform and removable singularities*From*: Roman <rschmied at gmail.com>*Date*: Sat, 28 Apr 2007 06:00:40 -0400 (EDT)*References*: <f0kbmk$qvt$1@smc.vnet.net><f0pk9v$1t0$1@smc.vnet.net>

David, Peter: I like this workaround best, using Peter's Piecewise[] function. Still, some manual work required, but pretty quick through defining something like fixfunction[f_,x0_] := With[{f0=Limit[f[x],x->x0]}, Piecewise[{{f0,x0}},f[#]]&] where you can just "fix" a function's removable singularity at x0, e.g., fixfunction[Sin[#]/#&, 0] Thanks for the help! Roman. On Apr 27, 11:21 am, Peter Pein <pet... at dordos.net> wrote: > 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