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
-- 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