A new approach to spectral factorization of a class of matrix-valued spectral densities

Hendra I. Nurdin

doi:10.1109/CDC.2005.1583110

A new approach to spectral factorization of a class of matrix-valued spectral densities

Hendra I. Nurdin^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Citations (Scopus)

Abstract

In this paper we propose a new approach to spectral factorization of a class of matrix-valued spectral densities. Our results are based on a recent necessary and sufficient uniform log-integrability condition for the canonical spectral factorization mapping to be sequentially continuous. In particular, we derive a new set of easily verifiable sufficient conditions for uniform log-integrability to hold. The proposed approach does not require the spectral density to be coercive, and the class to which it is applicable is reasonably large as to include many spectral densities which are of interest in applications. We also present a new spectral factorization algorithm for scalar analytic spectral densities along with a numerical example.

Original language	English
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	5929-5934
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2005.1583110
Publication status	Published - 2005
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Conference

Conference	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/Territory	Spain
City	Seville
Period	12/12/05 → 15/12/05

Access to Document

10.1109/CDC.2005.1583110

Cite this

Nurdin, H. I. (2005). A new approach to spectral factorization of a class of matrix-valued spectral densities. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 5929-5934). Article 1583110 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1583110

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title = "A new approach to spectral factorization of a class of matrix-valued spectral densities",

abstract = "In this paper we propose a new approach to spectral factorization of a class of matrix-valued spectral densities. Our results are based on a recent necessary and sufficient uniform log-integrability condition for the canonical spectral factorization mapping to be sequentially continuous. In particular, we derive a new set of easily verifiable sufficient conditions for uniform log-integrability to hold. The proposed approach does not require the spectral density to be coercive, and the class to which it is applicable is reasonably large as to include many spectral densities which are of interest in applications. We also present a new spectral factorization algorithm for scalar analytic spectral densities along with a numerical example.",

keywords = "Rational approximation, Rational covariance extension, Second order stochastic processes, Spectral factorization",

author = "Nurdin, {Hendra I.}",

year = "2005",

doi = "10.1109/CDC.2005.1583110",

language = "English",

isbn = "0780395689",

series = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

pages = "5929--5934",

booktitle = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

note = "44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 ; Conference date: 12-12-2005 Through 15-12-2005",

}

Nurdin, HI 2005, A new approach to spectral factorization of a class of matrix-valued spectral densities. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583110, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 5929-5934, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1583110

A new approach to spectral factorization of a class of matrix-valued spectral densities. / Nurdin, Hendra I.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 5929-5934 1583110 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this paper we propose a new approach to spectral factorization of a class of matrix-valued spectral densities. Our results are based on a recent necessary and sufficient uniform log-integrability condition for the canonical spectral factorization mapping to be sequentially continuous. In particular, we derive a new set of easily verifiable sufficient conditions for uniform log-integrability to hold. The proposed approach does not require the spectral density to be coercive, and the class to which it is applicable is reasonably large as to include many spectral densities which are of interest in applications. We also present a new spectral factorization algorithm for scalar analytic spectral densities along with a numerical example.

AB - In this paper we propose a new approach to spectral factorization of a class of matrix-valued spectral densities. Our results are based on a recent necessary and sufficient uniform log-integrability condition for the canonical spectral factorization mapping to be sequentially continuous. In particular, we derive a new set of easily verifiable sufficient conditions for uniform log-integrability to hold. The proposed approach does not require the spectral density to be coercive, and the class to which it is applicable is reasonably large as to include many spectral densities which are of interest in applications. We also present a new spectral factorization algorithm for scalar analytic spectral densities along with a numerical example.

KW - Rational approximation

KW - Rational covariance extension

KW - Second order stochastic processes

KW - Spectral factorization

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U2 - 10.1109/CDC.2005.1583110

DO - 10.1109/CDC.2005.1583110

M3 - Conference contribution

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SN - 9780780395688

T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

SP - 5929

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BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

T2 - 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

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Nurdin HI. A new approach to spectral factorization of a class of matrix-valued spectral densities. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 5929-5934. 1583110. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). doi: 10.1109/CDC.2005.1583110

A new approach to spectral factorization of a class of matrix-valued spectral densities

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