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
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