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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: [mg54054] Re: Fourier function...having problems reproducing answers in a paper
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Wed, 9 Feb 2005 09:27:27 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 2/8/05 at 5:31 AM, cire1611 at gmail.com (elparedblanco) wrote:


>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?

There are different conventions as to what to use for normalizing constants when doing a Fourier transform. Take a look at section 3.8.3 of the Mathematica Book or the information in the online documentation for Fourier for more details.

For your particular case, it appears the paper you are reading is a paper of signal processing since

In[1]:=
Fourier[{0.5,0,0.4,0,0,0.1}, FourierParameters -> {1, -1}]
Out[1]=
{1. + 0.*I, 0.35 - 
   0.2598076211353316*I, 
  0.24999999999999997 + 
   0.4330127018922193*I, 
  0.8 + 0.*I, 
  0.24999999999999997 - 
   0.4330127018922193*I, 
  0.35 + 0.2598076211353316*I}
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