Spectral factorization of time-varying covariance functions: The singular case

John B. Moore; Brian D.O. Anderson

doi:10.1007/BF01705880

Spectral factorization of time-varying covariance functions: The singular case

John B. Moore^*, Brian D.O. Anderson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

If a known linear system is excited by Gaussian white noise, the calculation of the output covariance of the system is relatively straightforward. This paper considers the harder converse problem, that of passing from a known covariance to a system which will generate it. The problem is solved for covariances R_y(t, τ) with |R_y(t, t)| < ∞ for all t and such that the y-process is Gauss-Markov, i.e., it may be obtained as the output of a linear finite-dimensional system excited by white noise.

Original language	English
Pages (from-to)	10-23
Number of pages	14
Journal	Mathematical Systems Theory
Volume	4
Issue number	1
DOIs	https://doi.org/10.1007/BF01705880
Publication status	Published - Mar 1970
Externally published	Yes

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title = "Spectral factorization of time-varying covariance functions: The singular case",

abstract = "If a known linear system is excited by Gaussian white noise, the calculation of the output covariance of the system is relatively straightforward. This paper considers the harder converse problem, that of passing from a known covariance to a system which will generate it. The problem is solved for covariances Ry(t, τ) with |Ry(t, t)| < ∞ for all t and such that the y-process is Gauss-Markov, i.e., it may be obtained as the output of a linear finite-dimensional system excited by white noise.",

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N2 - If a known linear system is excited by Gaussian white noise, the calculation of the output covariance of the system is relatively straightforward. This paper considers the harder converse problem, that of passing from a known covariance to a system which will generate it. The problem is solved for covariances Ry(t, τ) with |Ry(t, t)| < ∞ for all t and such that the y-process is Gauss-Markov, i.e., it may be obtained as the output of a linear finite-dimensional system excited by white noise.

AB - If a known linear system is excited by Gaussian white noise, the calculation of the output covariance of the system is relatively straightforward. This paper considers the harder converse problem, that of passing from a known covariance to a system which will generate it. The problem is solved for covariances Ry(t, τ) with |Ry(t, t)| < ∞ for all t and such that the y-process is Gauss-Markov, i.e., it may be obtained as the output of a linear finite-dimensional system excited by white noise.

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Spectral factorization of time-varying covariance functions: The singular case

Abstract

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