Re: FourierTransform

*To*: mathgroup at smc.vnet.net*Subject*: [mg57614] Re: FourierTransform*From*: "Mariusz Jankowski" <mjankowski at usm.maine.edu>*Date*: Thu, 2 Jun 2005 05:16:51 -0400 (EDT)*Organization*: University of Southern Maine*References*: <d7k36h$oi1$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Re: FourierTransform***From:*"Marcin Rak" <umrakmm@cc.umanitoba.ca>