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MathGroup Archive 2005

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Re: Fourier function...having problems reproducing answers in a paper

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54059] Re: Fourier function...having problems reproducing answers in a paper
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 9 Feb 2005 09:27:34 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <cua5b2$hh8$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <cua5b2$hh8$1 at smc.vnet.net>,
 "elparedblanco" <cire1611 at gmail.com> wrote:

> Hi there,
> 
> I am using the Fourier function on a simple list probability
> distribution {.5,0,.4,0,0,.1}.  The paper I'm reading says I should be
> geting an answer like this:
> 
> {1, .35-.2598i, .25+.433i, .8, .25-.433i, .35+.2598i}.
> 
> However this is what Mathematica is returning:
> 
> {.408248 + i,  .142887 + .106066i, .102062 - .176777i .326599 + i,
> .102062 + .17677i, .142887 - .106066i }
> 
> I assume that these are somehow equivilant.  Can some explain how/why?

If you compute

  ift = InverseFourier[{0.5, 0, 0.4, 0, 0, 0.1}]

and then normalize,

  Chop[ift Sqrt[Length[ift]]]

you get the same answer (up to numerical round-off) as the paper you're 
reading.

For an explanation, see page 218 of

 Crandall, R. 1991, Mathematica for the Sciences, 
 Addison-Wesley, Reading, Mass.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
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