Re: Fourier Transform Bug
- To: mathgroup at smc.vnet.net
- Subject: [mg63632] Re: [mg63604] Fourier Transform Bug
- From: Pratik Desai <pdesai1 at umbc.edu>
- Date: Sun, 8 Jan 2006 03:32:53 -0500 (EST)
- References: <200601070729.CAA06910@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?
>
>
>
No bug here atleast for 5.1
In[156]:=
$Version
checkratio[f_]:=FourierTransform[f[x],x,y,
FourierParameters\[Rule]{0,-2 Pi}]/FourierTransform[
f[x],x,y,FourierParameters\[Rule]{1,-2 Pi}];
ColumnForm[{checkratio[#&],checkratio[#^2&],checkratio[Exp[-#^2]&],
checkratio[DiracDelta],checkratio[#*Exp[-#^2]&]}]//InputForm
Out[156]=
5.1 for Microsoft Windows (January 27, 2005)
Out[158]//InputForm=
1/Sqrt[2*Pi]
1/Sqrt[2*Pi]
1/Sqrt[2*Pi]
1/Sqrt[2*Pi]
1/Sqrt[2*Pi]
Hope this helps
Pratik
- References:
- Fourier Transform Bug
- From: "irchans" <infinitgames@yahoo.com>
- Fourier Transform Bug