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: firstname.lastname@example.org
- References: <email@example.com>
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:= FourierTransform[ HeavisideTheta[a - Abs[t]], t, w, Assumptions -> a > 0 ] Out= -((I E^(-I a w) (-1 + E^(2 I a w)))/(Sqrt[2 \[Pi]] w)) In:= % // Simplify Out= (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.