FourierTransform[Sign[t], t, w, FourierParameters -> {1, -1}]
- To: mathgroup at smc.vnet.net
- Subject: [mg21368] FourierTransform[Sign[t], t, w, FourierParameters -> {1, -1}]
- From: "Jordan Rosenthal" <jr at ece.gatech.edu>
- Date: Wed, 29 Dec 1999 23:18:42 -0500 (EST)
- Organization: Georgia Institute of Technology, Atlanta GA, USA
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
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.
Thanks,
- Jordan