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MathGroup Archive 2000

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Fourier Question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25623] Fourier Question
  • From: xxx at uunet.uu.net
  • Date: Mon, 16 Oct 2000 03:04:43 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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.







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