Spectrum estimation and harmonic analysis. Thomson, D. Proceedings of the IEEE, 70(9):1055–1096, 1982. ISBN: 0018-9219doi abstract bibtex 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.
@article{Thomson1982,
title = {Spectrum estimation and harmonic analysis},
volume = {70},
issn = {0018-9219},
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.},
number = {9},
journal = {Proceedings of the IEEE},
author = {Thomson, D.J.},
year = {1982},
note = {ISBN: 0018-9219},
keywords = {\#nosource},
pages = {1055--1096},
}
Downloads: 0
{"_id":"ikmFMa9PnNjqBnkEg","bibbaseid":"thomson-spectrumestimationandharmonicanalysis-1982","author_short":["Thomson, D."],"bibdata":{"bibtype":"article","type":"article","title":"Spectrum estimation and harmonic analysis","volume":"70","issn":"0018-9219","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.","number":"9","journal":"Proceedings of the IEEE","author":[{"propositions":[],"lastnames":["Thomson"],"firstnames":["D.J."],"suffixes":[]}],"year":"1982","note":"ISBN: 0018-9219","keywords":"#nosource","pages":"1055–1096","bibtex":"@article{Thomson1982,\n\ttitle = {Spectrum estimation and harmonic analysis},\n\tvolume = {70},\n\tissn = {0018-9219},\n\tdoi = {10.1109/PROC.1982.12433},\n\tabstract = {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.},\n\tnumber = {9},\n\tjournal = {Proceedings of the IEEE},\n\tauthor = {Thomson, D.J.},\n\tyear = {1982},\n\tnote = {ISBN: 0018-9219},\n\tkeywords = {\\#nosource},\n\tpages = {1055--1096},\n}\n\n","author_short":["Thomson, D."],"key":"Thomson1982","id":"Thomson1982","bibbaseid":"thomson-spectrumestimationandharmonicanalysis-1982","role":"author","urls":{},"keyword":["#nosource"],"metadata":{"authorlinks":{}}},"bibtype":"article","biburl":"https://bibbase.org/zotero/sumbre","dataSources":["FTTT6MtwhkNF2aJCF"],"keywords":["#nosource"],"search_terms":["spectrum","estimation","harmonic","analysis","thomson"],"title":"Spectrum estimation and harmonic analysis","year":1982}