Re: Fourier Transform Bug
- To: mathgroup at smc.vnet.net
- Subject: [mg63630] Re: [mg63604] Fourier Transform Bug
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sun, 8 Jan 2006 03:32:50 -0500 (EST)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
$Version
5.2 for Mac OS X (June 20, 2005)
checkratio[f_]:=
FourierTransform[f[x],x,y,FourierParameters->{0,-2 Pi}]/
FourierTransform[f[x],x,y,FourierParameters->{1,-2 Pi}];
checkratio[#&]==checkratio[#^2&]==checkratio[Exp[-#^2]&]==
checkratio[DiracDelta]==checkratio[#*Exp[-#^2]&]==1/Sqrt[2Pi]
True
Bob Hanlon
>
> From: "irchans" <infinitgames at yahoo.com>
To: mathgroup at smc.vnet.net
> Subject: [mg63630] [mg63604] Fourier Transform Bug
>
> 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?
>
>