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FourierTransform[Sign[t], t, w, FourierParameters -> {1, -1}]

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  • Subject: [mg21368] FourierTransform[Sign[t], t, w, FourierParameters -> {1, -1}]
  • From: "Jordan Rosenthal" <jr at>
  • Date: Wed, 29 Dec 1999 23:18:42 -0500 (EST)
  • Organization: Georgia Institute of Technology, Atlanta GA, USA
  • Sender: owner-wri-mathgroup at


I have only been using Mathematica for under a month and have a question.  I
was trying to reproduce the results of some well known Fourier transforms
(allowing distributions) in Mathematica.  For instance,

    sgn(t)     <---------->     2/(j*w)

where j = sqrt(-1).  (See, for example "The Fourier Integral and its
Applications", Papoulis).  So I ran the following code

  FourierTransform[Sign[t], t, w, FourierParameters -> {1, -1}]

and got the following result

  \!\(\(-2\)\ \[Pi]\ DiracDelta[w] +
      2\ \((\(-\(\[ImaginaryI]\/w\)\) - \[Pi]\ DiracDelta[w])\)\)

Some questions:

1) Why does the answer not match what I expect?  Am I missing an assumption
somewhere or using something wrong?

2) In the result given by Mathematica, two of the terms obviously combine so
I tried to use  / /Simplify after the input, but it didn't simplify this
rather "simple" term.  Why?  (I know I can use / /Expand to get it to
simplify, but was just surprised that / /Simplify didn't work).

Minor question:  Is there a better way to copy an output into a posting?
All those backslashes seem to be a bit confusing.


- Jordan

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