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.