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).