Andries,
It depends on what you're trying to accomplish. Using a limited number of
Fourier coefficients (presumably the first few) is what is known as
"low-pass filtering in the frequency domain". It will reproduce the broader
features of your time series, while cutting out sharp transitions and some
of the "noise"--random variability from one data point to the next.
Abruptly truncating a Fourier series can lead to distortion when you try to
reconstruct your time series. You can get oscillations, overshoot, and
error known as "Gibbs phenomenon". (Scary memories of my college EE courses
are coming back now.) Depending on your application, a better approach may
be to gradually weight some of the Fourier coefficients from one down to
zero as you go along the list, after which all the rest are given zero
weight. There is a whole science to this weighting, which again depends on
exactly what you are trying to accomplish. To get started, Google the term
"Hamming window", and dig in from there.
Enjoy!
Alan
Alan Hochberg
Vice President, Research
ProSanos Corp.
225 Market Street
Suite 502
Harrisburg, PA 17101
Tel. 717-635-2124
Fax 717-635-2575
alan.hochberg@prosanos.com
www.prosanos.com
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