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Re: FourierTransform[Sign[t], t, w, FourierParameters -> {1, -1}]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg21386] Re: FourierTransform[Sign[t], t, w, FourierParameters -> {1, -1}]
*From*: "Kevin J. McCann" <kevinmccann at home.com>
*Date*: Sat, 1 Jan 2000 20:54:45 -0500 (EST)
*References*: <84eme9$60s@smc.vnet.net> <84jovk$e2n@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Note that if you drop the FourierParameters option, you get the correct
answer, i.e. no delta-function.
Kevin
> In article <84eme9$60s at smc.vnet.net>, "Jordan Rosenthal"
> <jr at ece.gatech.edu> wrote:
>
> > 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).
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