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Re: FourierTransform on UnitStep

• To: mathgroup at smc.vnet.net
• Subject: [mg14473] Re: FourierTransform on UnitStep
• From: John Doty <jpd at w-d.org>
• Date: Fri, 23 Oct 1998 20:58:51 -0400
• Organization: Wampler-Doty Family
• References: <70k58j$eon@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Normand Leclerc wrote:

>   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

There are two conventions for the sign of I in Fourier analysis: the
"physics" convention, and the "EE" convention. Mathematica uses the
"physics" convention.

If you set:

$FourierFrequencyConstant = -1

you'll get the behavior you want.

This clash of conventions often causes serious headaches. I have heard
that a certain array processor manufacturer once, in response to a
customer complaint, changed their firmware to use the "correct"
convention (according to that customer), without changing the
documentation or otherwise disseminating news of this change. As a
result, geologists interpreting the first synthetic aperture radar maps
of Venus from the Magellan mission struggled to find a geological
explanation for unexpected small-scale smoothness of the planet (the
problem was eventually discovered).

Be careful!

-- 
John Doty		"You can't confuse me, that's my job." Home: jpd at w-d.org
Work: jpd at space.mit.edu