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