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.