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Re: Fourier Question

• To: mathgroup at smc.vnet.net
• Subject: [mg25653] Re: Fourier Question
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 18 Oct 2000 02:52:25 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <8seaq8$6s8@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

Fourier[] make a discrete Fourier transform of equal sampled data
on the interval [0,2Pi). It make a comples to complex transform
i.e. with basis functions Exp[i k t] and not Cos[] or Sin[] only.

A nice introduction text about discret Fourier transform may be
at:

http://www.ulib.org/webRoot/Books/Numerical_Recipes/bookcpdf.html

chapter 12.

Mathematica is clearly much smarter than the NR functions but the
text is very clear.

Regards
  Jens

xxx at uunet.uu.net wrote:
> 
> Hello.  I am reading a few books on Fourier Analysis, and I am stuck on
> understanding a few concepts.
> I was hoping someone who uses this function in Mathematica could point me in
> the right direction.
> 
> To make it simple, suppose I have 4 sample points:
> 
> data = {1, 3, 2, 4}
> 
> Fourier[data, FourierParameters -> {-1, 1}] // Chop
> 
> This returns:
> 
> {2.5, -0.25 - 0.25 \[ImaginaryI], -1., -0.25 + 0.25 \[ImaginaryI]}
> 
> I am not sure how to interpret the results.
> The best I understand is:
> 
> results = 2.5 + (-.25-.25 I ) Cos[1 t] -1 Sin [ 1 t] +  (-.25 + .25 I Cos
>  2 t]...
> 
> As you can tell, I am sure this is not correct.
> Could someone point me in the right direction.  I am sure I will figure it
> out from there once I understand  how the results are used.
> 
> I  am using FourierParameters -> {-1, 1}  because I am mostly doing data
> analysis.
> Thank  you in advance for any insight.  Dana.