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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
The University of Western Australia
Nedlands WA 6907 mailto:paul at physics.uwa.edu.au
AUSTRALIA http://physics.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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