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Re: Fourier Transform Bug

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63648] Re: Fourier Transform Bug
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Mon, 9 Jan 2006 04:48:24 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <dpnr1t$6sd$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

irchans wrote:
> The fourier transform for mathematica version 5.0 does not seem get the
> correct result when using FourierParameters with the product of x and
> Exp[-x^2].   According to the documentation, the following ratio should
> always be 1/ Sqrt[2 Pi].
> 
> checkratio[f_] := FourierTransform[ f[x], x, y, FourierParameters ->
> {0, -2 Pi}]/
>     FourierTransform[  f[x], x, y, FourierParameters -> {1, -2 Pi}];
> 
> In fact, the following expressions correctly evaluate to 1/ Sqrt[ 2
> Pi]:
> 
> checkratio[# &]
> checkratio[#^2 &]
> checkratio[Exp[-#^2] & ]
> checkratio[DiracDelta]
> 
> But,
> 
> checkratio[#*Exp[-#^2] & ]
> 
> evaluates to 1/ 2/Pi which is incorrect.  Can anyone else repoduce this
> bug?
> 

Nothing unusual here.

In[1]:=
$Version

Out[1]=
"5.2 for Microsoft Windows (June 20, 2005)"

In[2]:=
checkratio[f_] := FourierTransform[f[x], x, y,
      FourierParameters -> {0, -2*Pi}]/FourierTransform[f[x], x, y,
      FourierParameters -> {1, -2*Pi}];

In[3]:=
checkratio[#1 & ]
checkratio[#1^2 & ]
checkratio[Exp[-#1^2] & ]
checkratio[DiracDelta]

Out[3]=
1/Sqrt[2*Pi]

Out[4]=
1/Sqrt[2*Pi]

Out[5]=
1/Sqrt[2*Pi]

Out[6]=
1/Sqrt[2*Pi]

In[7]:=
checkratio[#1*Exp[-#1^2] & ]

Out[7]=
1/Sqrt[2*Pi]

Best regards,
/J.M.


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