Spectrum estimation and harmonic analysis
Proceedings of the IEEE, 70 (9):
1055--1096 (1982)DOI: 10.1109/PROC.1982.12433
Abstract
In the choice of an estimator for the spectrum of a stationary time
series from a finite sample of the process, the problems of bias
control and consistency, or "smoothing," are dominant. In this paper
we present a new method based on a "local" eigenexpansion to estimate
the spectrum in terms of the solution of an integral equation. Computationally
this method is equivalent to using the weishted average of a series
of direct-spectrum estimates based on orthogonal data windows (discrete
prolate spheroidal sequences) to treat both the bias and smoothing
problems. Some of the attractive features of this estimate are: there
are no arbitrary windows; it is a small sample theory; it is consistent;
it provides an analysis-of-variance test for line components; and
it has high resolution. We also show relations of this estimate to
maximum-likelihood estimates, show that the estimation capacity of
the estimate is high, and show applications to coherence and polyspectrum
estimates.
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