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MathGroup Archive 1999

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Re: Problem with the zero-term of Fourier[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19634] Re: Problem with the zero-term of Fourier[]
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Mon, 6 Sep 1999 04:20:47 -0400
  • Organization: University of Western Australia
  • References: <7qsftj$17c@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hans Steffani wrote:

> If have a long list of measured values in ixr.
> (Plus@@ixr)/Sqrt[Length[ixr]]
> gives
> -146.263
>
> but
> Fourier[ixr][[1]]
> gives
> -56.1317-3.03437 I
>
> which is complex although it should be real (ixr is a list of
> real numbers) and it is different from the first term althugh
> it should be the same.

Assuming that ixr is real then I can only guess that the problem
arises from the bug with packed arrays of complex numbers?

I don't see this behaviour though. For the list

In[1]:= ixr=Table[Random[], {20000}];

here is the DC term,

In[2]:= Plus @@ ixr/Length[ixr]
Out[2]= 0.498249

which agrees with the Fourier result:

In[3]:= Chop[Fourier[ixr][[1]]/Sqrt[Length[ixr]]]
Out[3]= 0.498249

> I also tried
> 1/Sqrt[Length[ixr]] *
>   Sum[ixr[[tau]] Exp[2 Pi I(tau-1)(1-1)/Length[ixr]],{tau,Length[ixr]}]
> which also gives -146.263

In[4]:= Sum[ixr[[tau]]*E^((2*Pi*I[tau - 1]*(1 - 1))/Length[ixr]),
   {tau, 1, Length[ixr]}]/Length[ixr]
Out[4]= 0.498249

> What is the problem?

You need to use the appropriate normalization in each case.

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
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AUSTRALIA                            http://physics.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
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