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Re: FourierTransform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96023] Re: FourierTransform
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sun, 1 Feb 2009 04:43:06 -0500 (EST)
  • References: <gm1dks$3nk$1@smc.vnet.net>

Hi,

the Fourier transform over the interval x in (-Infinity,Infinity)
converges only for quadratic integrable functions, i.e., functions
where Integrate[Conjugate[f[x]]*f[x],{x,-Infinity,Infinity}]< Infinity

This is not the case for Cosh[x], and so no Fourier transform exist.

I always thought that one should learn this, before one start to use
a computer algebra.

Regards
   Jens

Fabian wrote:
> I just got the new version (7.0) of Mathematica and was full of hope
> that the function FourierTransform is finally improved. (If you have no
> idea what I'm talking about try FourierTransform[Cosh[x],x,t] on
> Mathematica 6) It turns out that the developers have added support
> for the Human Genome project but did not manage to improve the basic
> mathematical functions considerably. For example try:
> 
>  FourierTransform[1/Cosh[a x],x,t]
> 
> Any ideas why this is the case? I always thought that an average user
> is more into Fourier transformation than into image processing?
> 
> Cheers,
>   Fabian
> 


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