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Re: Fourier Transform

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  • Subject: [mg124266] Re: Fourier Transform
  • From: "Oleksandr Rasputinov" <oleksandr_rasputinov at>
  • Date: Sat, 14 Jan 2012 17:16:39 -0500 (EST)
  • Delivered-to:
  • References: <jercl1$1d8$>

On Sat, 14 Jan 2012 07:59:29 -0000, <jstorch at> 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  )


  HeavisideTheta[a - Abs[t]], t, w,
  Assumptions -> a > 0

-((I E^(-I a w) (-1 + E^(2 I a w)))/(Sqrt[2 \[Pi]] w))

% // Simplify

(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.

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