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Spectrum estimation and harmonic analysis
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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Metadata
- Authors
- Thomson, D. J.
- Venue
- Proceedings of the IEEE
- Published
- 1982
- Volume
- 70
- Issue
- 9
- Pages
- 1055-1096
- ISSN
- 0018-9219 (ISSN-L)
- OpenAlex
- W2155722796
- Cited by
- 4,418
- References
- 5
- FWCI
- 8.78
- Type
- journal article
- Language
- en
- Open access
- closed
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