Re: Re: FourierTransform
- To: mathgroup at smc.vnet.net
- Subject: [mg57864] Re: Re: FourierTransform
- From: "Marcin Rak" <umrakmm at cc.umanitoba.ca>
- Date: Fri, 10 Jun 2005 02:29:35 -0400 (EDT)
- References: <d7k36h$oi1$1@smc.vnet.net> <200506020916.FAA11878@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Panie Mariuszu Well, the book you suggested seems to be extremely popular with the engineers at the university, so I can't say that I've had the luck to have a look at it yet, however, seeing how you were kind enough to even provide me with the page, I don't think I'll have to worry too much. I'm still trying to prove this on my own, and I am getting closer, but I think I'll probably manage to get a hold of that book before I actually figure it out. So, as they say, przepraszam for the delay. Pozdrowienia z zimnej kanady Marcin ----- Original Message ----- From: "Mariusz Jankowski" <mjankowski at usm.maine.edu> To: mathgroup at smc.vnet.net Subject: [mg57864] Re: FourierTransform > Panie Marcinie, > > The two forms of evaluation give different results because the Fourier > integral does not converge for the case of the unit step function (violates > the so-called Dirichlet conditions) and thus cannot be obtained by direct > evaluation of the integral. However, using the integration property of the > FT you can, at least indirectly, obtain the result you show below (Oppenheim > and Willsky, "Signals and Systems," page 307). > > > Pozdrawiam, Mariusz > > > > > > >>> Marcin Rak<umrakmm at cc.umanitoba.ca> 06/01/05 6:38 AM >>> > > Hi, > > I was wondering what the exact mathematica equation of the following > Mathematica Command was: > > FourierTransform[UnitStep[t],t,w,FourierParameters->{1,-1}] > > This gives -i/w + pie*DiracDelta[w] > > which is correct. However, when I substitute my UnitStep[t] function > into the direct definition employed by FourierTransform, I don't get the > same result. ie > > Integrate[UnitStep[t]*Exp[-i*w*t],{t,-infinity,infinity}] Doesn't give > the same result, despite the fact that in section 3.5.11 of the > Mathematica book it is defined as such? > > Thanks > MR > > > >
- References:
- Re: FourierTransform
- From: "Mariusz Jankowski" <mjankowski@usm.maine.edu>
- Re: FourierTransform