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MathGroup Archive 2005

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FourierTransform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57585] FourierTransform
  • From: "Marcin Rak" <umrakmm at cc.umanitoba.ca>
  • Date: Wed, 1 Jun 2005 06:04:03 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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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