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Re: Fourier Transform

• To: mathgroup at smc.vnet.net
• Subject: [mg13727] Re: Fourier Transform
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 19 Aug 1998 01:38:19 -0400
• Organization: University of Western Australia
• References: <6r107l$fih@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Edward Neuman wrote:
 
> Let f(x) = 1/x. If f is regarded as the generalized function, then its
> Fourier transform is:
>                                   -Pi*I*Sign[t] (see, e.g., G.B.
> Folland, "Fourier Analysis and Its Applications," p. 337).
> Using Mathematica 3.0 we get:
> In[1]:=
> << "Calculus`FourierTransform`"
> 
> In[2]:=
> FourierTransform[1/x, x, t]
> 
> Out[2]=
> 2*I*Pi*(-(1/2) + UnitStep[t, ZeroValue -> 1/2]).
> 
> This agrees with the above result only if t = 0. Bug?

No, feature. To handle al the definitions of the FT in the literature,
the version 3.0 package has two parameters, FourierFrequencyConstant
and FourierOverallConstant.

?FourierFrequencyConstant
"FourierFrequencyConstant is an option for FourierTransform and related
functions that specifies the constant multiplying I w t in the
definition of FourierTransform.  The default value of
FourierFrequencyConstant is $FourierFrequencyConstant." 

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul at physics.uwa.edu.au  AUSTRALIA                       
http://www.physics.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
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