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Some Recent Developments in Spectrum and Harmonic Analysis

In: Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface

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  • David J. Thomson

    (Bell Laboratories)

Abstract

In estimating the spectrum of a stationary time series from a finite sample of the process two problems have traditionally been dominant: first, what algorithm should be used so that the resulting estimate is not severely biased; and second, how should one “smooth” the estimate so that the results are consistent and statistically significant. Within the class of spectrum estimation procedures that have been found successful in the various engineering problems considered, bias control is achieved by iterative model formation and prewhitening combined with robust procedures ( the “robust filter” ), while “smoothing” is done by an adaptive nonlinear method. Recently a method has been found which, by using a “local” principal components expansion to estimate the spectrum, provides new solutions to both the bias and smoothing problems and also permits a unification of the differences between windowed and unwindowed philosophies. This estimate, which is an approximate solution of an integral equation, consists of a weighted average of a series of direct spectrum estimates made using discrete prolate spheroidal sequences as orthogonal data windows.

Suggested Citation

  • David J. Thomson, 1981. "Some Recent Developments in Spectrum and Harmonic Analysis," Springer Books, in: William F. Eddy (ed.), Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, pages 167-171, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-9464-8_24
    DOI: 10.1007/978-1-4613-9464-8_24
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