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[1]:=
<< Calculus`FourierTransform`
In[3]:=
Options[FourierTransform]
Out[3]=
{FourierFrequencyConstant -> 1,
FourierOverallConstant -> 1, DefiniteIntegral -> False,
Assumptions -> {}}
Change the Fourier frequency constant to -1.
In[4]:=
FourierTransform[UnitStep[t], t, w,
FourierFrequencyConstant -> -1]
Out[4]=
-(I/w) + Pi*DiracDelta[w]
Edward Neuman