Re: FourierTransform[Sign[t], t, w, FourierParameters -> {1, -1}]
- To: mathgroup at smc.vnet.net
- Subject: [mg21399] Re: FourierTransform[Sign[t], t, w, FourierParameters -> {1, -1}]
- From: "Jordan Rosenthal" <jr at ece.gatech.edu>
- Date: Tue, 4 Jan 2000 02:12:32 -0500 (EST)
- Organization: Georgia Institute of Technology, Atlanta GA, USA
- References: <84eme9$60s@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, Thanks to all for the various responses both here on the newsgroup and via private email. Conclusion: ------------------------------- There appears to be a bug that occurs when using the FourierParameters with a negative value for b. A possible workaround: ----------------------------------- If the signal is real, use positive value for b and conjugate the result. If the signal is complex, also conjugate the signal before taking the transform. Thanks again, - Jordan "Jordan Rosenthal" <jr at ece.gatech.edu> wrote in message news:84eme9$60s at smc.vnet.net... > 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 > > > > > > > > > > > >