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MathGroup Archive 2007

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Re: FourierTransform of Sign^2 ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80163] Re: FourierTransform of Sign^2 ?
  • From: Hendrik van Hees <hees at comp.tamu.edu>
  • Date: Tue, 14 Aug 2007 06:57:38 -0400 (EDT)
  • Organization: Texas A&M University
  • References: <f9p6c7$rvv$1@smc.vnet.net>

Dana DeLouis wrote:

>> Mathematica (v. 5.0, Mac) gives
>> -Sqrt[2 Pi]*DiracDelta[q]
>> with a minus sign.
> 
> There was a discussion in another group recently about 5.2 with something
> similar.  I'm not sure what the correct answer is, but I thought you might
> find this interesting.
> 
> equ = Sech[x*a];
> 
> 5.2 takes about 1 minute to do this...
> 
> (* 5.2 *)
> 
> Timing[FourierTransform[equ,  x, s]]
> 
> {55.594,
>    (Sqrt[Pi/2]*Sech[(Pi*s)/ (2*a)])/a}

Again, to check against my ancient 4.0:

Mathematica 4.0 for Students: Linux Version
Copyright 1988-1999 Wolfram Research, Inc.
 -- Motif graphics initialized -- 

In[1]:= equ=Sech[x*a];

In[2]:= Timing[FourierTransform[equ,  x, s]]

                           Pi       Pi s
                      Sqrt[--] Sech[----]
                           2        2 a
Out[2]= {1.82 Second, -------------------}
                               a
It seems that version 5.2 gives the same solution as 4.0, but takes longer.
Perhaps we have to check whether 5.2 and 4.0 or 6.0 gives the correct
answer by hand?

-- 
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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