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MathGroup Archive 2001

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Frequency analysis of quasiperiodic Functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27076] Frequency analysis of quasiperiodic Functions
  • From: "Dieter Eichrodt" <eichrodt at eircom.net>
  • Date: Sat, 3 Feb 2001 04:59:11 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Given is a function of time as a table of n datapoints which is to be
interpolated by a trigonometric series :
y[t]=a0+Sum[a[[i]]*Cos[2 Pi*f[[i]]*t/n],{i,k}]+Sum[b[[i]]*Sin[2
Pi*f[[i]]*t/n],{i,k}];

--with k=2 n/3-1   in order to have the same number of output data as input
data.

How can the {a}, {b}, {f} for a best fit be calculated using Mathematica ?

Note that the frequencies {f} are not integer multiples of some basic
frequency, in which case a simple Fourier series would fitt.

Dieter Eichrodt                                 eichrodt at eircom.net




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