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MathGroup Archive 2007

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Re: FourierTransform of Sign^2 ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80041] Re: FourierTransform of Sign^2 ?
  • From: Hendrik van Hees <hees at comp.tamu.edu>
  • Date: Sat, 11 Aug 2007 02:09:05 -0400 (EDT)
  • Organization: Texas A&M University
  • 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?

If it's of any interest. I've a pretty old version of Mathematica (4.0
Student Version), and I get the right result only after manual intervention
simplifying UnitStep[y]^2 to UnitStep[y]:

In[1]:= FourierTransform[Sign[y]^2, y, q] /. {UnitStep[y]^2 -> UnitStep[y]} 

Out[1]= Sqrt[2 Pi] DiracDelta[q]


-- 
Hendrik van Hees                        Texas A&M University
Phone:  +1 979/845-1411                 Cyclotron Institute, MS-3366
Fax:    +1 979/845-1899                 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/faq       mailto:hees at comp.tamu.edu


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