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Re: FourierTransform of Sign^2 ?

• To: mathgroup at smc.vnet.net
• Subject: [mg80014] Re: FourierTransform of Sign^2 ?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 10 Aug 2007 06:41:30 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <f9gv9e$b82$1@smc.vnet.net>

Jung-Tsung Shen wrote:
> I tried to evaluate the following Fourier Transform:
> 
> FourierTransform[Sign[y] Sign[y], y, q]
> 
> where Sign is the sign function. Instead of Sqrt[2 Pi]*DiracDelta[q],
> Mathematica (v. 5.0, Mac) gives
> 
> -Sqrt[2 Pi]*DiracDelta[q]
> 
> with a minus sign. Is this a bug or I am doing something wrong here?

Might be not of great help here, but Mathematica 5.2 and 6.0.1 both 
return the expected results.

In[1]:=
$Version
FourierTransform[Sign[y]*Sign[y], y, q]

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

Out[2]=
Sqrt[2 Pi] DiracDelta[q]

In[1]:=
$Version
FourierTransform[Sign[y]*Sign[y], y, q]

Out[1]= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)"

Out[2]= Sqrt[2 Pi] DiracDelta[q]

-- 
Jean-Marc