🚀 go-pugleaf

In article <Bu6CKC.6tF@me.utoronto.ca> steinman@me.utoronto.ca (David Steinman) writes:
>kavuri@lips.ecn.purdue.edu (Surya N Kavuri ) writes:

>>  When the data is NOT sampled at regular intervals, how are the fourier
>>  coefficients determined ?

>Well, it may not be pretty (or even that accurate), but I usually just
>integrate the coefficient integrals using a trapezoidal rule.  

There are three cases of interest that I can think of:

(a) The sampling is completely irregular.
(b) The sampling is perturbed from periodic.
(c) The sampling is a replication of a fixed irregular sample.

Case (a) can be handled by a large least squares matrix, but is
practically handled by integration.

Case (b) can be handled by a linear perturbation technique.

Case (c) can be handled by a least squares solution with the the
irregular sample combined with standard equal interval fourier
transform outside the interval.

An example of case (c) is measurements taken during daylight hours
at fixed times every day.

Details are left as an exercise for the reader.
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Richard Harter: SMDS Inc.  Net address: rh@smds.com Phone: 508-369-7398 
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