Re: Fourier Transform

*To*: mathgroup at smc.vnet.net*Subject*: [mg124266] Re: Fourier Transform*From*: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>*Date*: Sat, 14 Jan 2012 17:16:39 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jercl1$1d8$1@smc.vnet.net>

On Sat, 14 Jan 2012 07:59:29 -0000, <jstorch at earthlink.net> wrote: > Mathematica hangs when trying to evaluate the simple Fourier Transform > of H(a-|t|). > > FourierTransform[HeavisideTheta[a-abs[t]],t,w,Assumptions->a>0] > > (The answer should be Sqrt(2/Pi) (Sin[w a])/w ) > Typo. In[1]:= FourierTransform[ HeavisideTheta[a - Abs[t]], t, w, Assumptions -> a > 0 ] Out[1]= -((I E^(-I a w) (-1 + E^(2 I a w)))/(Sqrt[2 \[Pi]] w)) In[2]:= % // Simplify Out[2]= (Sqrt[2/Pi] Sin[a w])/w By the way, even with undefined abs[t], Mathematica doesn't hang. You just didn't give it long enough to figure out that it can't produce a useful result for the FT of H(a-f(t)) where f is an arbitrary function. In version 7 this takes about 30 seconds and in version 8 about two minutes on my computer.