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MathGroup Archive 2006

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Re: Re: Fourier Transforms

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64815] Re: [mg64789] Re: [mg64762] Fourier Transforms
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Sat, 4 Mar 2006 02:35:30 -0500 (EST)
  • References: <200603021148.GAA05247@smc.vnet.net> <200603030028.TAA29268@smc.vnet.net> <76e8f8180603030623y1d8ee0eftc74258212b9b2be@mail.gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

On Mar 3, 2006, at 9:23 AM, bsyehuda at gmail.com wrote:

> I really cannot figure out how you got the 0 expression
> both are unevaluated.

I pasted the results from running this on Mathematica v5.0 on Max OS  
X 10.4.5.  I did not do any analysis of the expressions.

> To Ben C.
> I see that these are odd functions, pointing the the functions in  
> the x domain are not real. are you aware of that fact?

Only the first expression is odd, the second is even.

> In addition, if this is the spectrum of some function, it should  
> include infinite energy, pointing on its behaviour (the spectrum is  
> not band-limited) (dirac delta, or some infinite value near the  
> origin)

You are correct that the Inverse Fourier Transform of the first  
expression should have some energy, perhaps this is a bug in version 5?

> Some coarse approximation:
> both function have a general form of a sign function

The second  expression actually looks like a Gaussian or Lorentzian.   
I would expect its spectrum to look like some kind of decaying sinusoid.

Regards,

Ssezi


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