       Re: FourierTransform on UnitStep

• To: mathgroup at smc.vnet.net
• Subject: [mg14503] Re: FourierTransform on UnitStep
• From: Edward Neuman <edneuman at siu.edu>
• Date: Fri, 23 Oct 1998 20:59:21 -0400
• Organization: SIUC
• References: <70k58j\$eon@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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 ele.etsmtl.ca

Normand,

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:

In:=
<< Calculus`FourierTransform`

In:=
Options[FourierTransform]
Out=
{FourierFrequencyConstant -> 1,
FourierOverallConstant -> 1, DefiniteIntegral -> False,
Assumptions -> {}}

Change the Fourier frequency constant to -1.

In:=
FourierTransform[UnitStep[t], t, w,
FourierFrequencyConstant -> -1]

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

Edward Neuman

```

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