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MathGroup Archive 2005

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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
>
>
>
>


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