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MathGroup Archive 2007

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Re: FourierTransform of Sign^2 ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80140] Re: FourierTransform of Sign^2 ?
  • From: "Dana DeLouis" <dana.del at gmail.com>
  • Date: Mon, 13 Aug 2007 04:40:33 -0400 (EDT)

> 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}

In Ver 6.0, we get a Minus sign.  I thought it was ver 6.0 that has the bug,
but I'm not sure of the correct answer.
We do note that it is much faster in 6.0 though.

(* 6.0.1 *)

Timing[FourierTransform[equ, x, s]]

{0.703, 
   -((Sqrt[Pi/2]*Sech[(Pi*s)/ (2*a)])/a)}

The real discussion focused on the fact that if you change 'a to a number
like Log[2], then FourierTransform does not work.

Ie
FourierTransform[Sech[x*Log[2]], x, s]

Unevaluated after a long long time.
-- 
Dana 
Windows XP & Mathematica 5.2


"Jung-Tsung Shen" <jushen at gmail.com> wrote in message
news:f9gv9e$b82$1 at smc.vnet.net...
>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?
> 
> Thanks.
> 
> JT
>



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