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Re: FourierTransform on UnitStep

  • To: mathgroup at
  • Subject: [mg14503] Re: FourierTransform on UnitStep
  • From: Edward Neuman <edneuman at>
  • Date: Fri, 23 Oct 1998 20:59:21 -0400
  • Organization: SIUC
  • References: <70k58j$>
  • Sender: owner-wri-mathgroup at

Normand Leclerc wrote:

> Hi,
>   I am a new EE Student and I'm just begining with Fourier transforms. I
> was using Mathematica at school when I saw something I just couldn't
> figure out.
>   FourierTransform[UnitStep[t],t,w] gives me I/w + pi DiracDelta[w]
>   I learned that it should give me pi DiracDelta[w]-I/w or 1/Iw + pi
> DiracDelta[w].
> Am I missing something or is there a bug in the FourierTransform
> package?  They are using Mathematica 3.0
> Normand Leclerc
> lecn1306 at


There is no bug in the `FourierTransform` package. Definition of the
integral Fourier transform leaves a room for specification of the
Fourier frequency constant. In some books it is defined either as 1 or
-1 or 2 or -2.
Try this:

<< Calculus`FourierTransform`

{FourierFrequencyConstant -> 1,
  FourierOverallConstant -> 1, DefiniteIntegral -> False,
  Assumptions -> {}}

Change the Fourier frequency constant to -1.

FourierTransform[UnitStep[t], t, w,
   FourierFrequencyConstant -> -1]

-(I/w) + Pi*DiracDelta[w]

Edward Neuman

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