Polyspectral analysis of mixed processes and coupled harmonics

Guotong Zhou; Georgios R. Giannakis

doi:10.1109/18.490556

Polyspectral analysis of mixed processes and coupled harmonics

Guotong Zhou, Georgios R. Giannakis

Electrical and Computer Engineering

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

37 Scopus citations

Abstract

Polyspectral analysis of processes with mixed spectra is considered, and scaled polyperiodograms are introduced to clarify issues related to stalionarity, ergodicity, and suppression of additive stationary noise in harmonic retrieval problems. Spectral and polyspectral approaches are capable of retrieving (un)coupled harmonics, not only when the harmonics have constant amplitudes, but also when they are observed in nonzero mean multiplicative noise. Fourier series polyspectra and asymptotic properties of scaled polyperiodograms provide general tools for higher order analysis of time series with mixed spectra. A single record phase coupling detector is derived to obviate the assumption of independent multiple records required by existing methods. The novelties are illustrated by simulation examples.

Original language	English (US)
Pages (from-to)	943-958
Number of pages	16
Journal	IEEE Transactions on Information Theory
Volume	42
Issue number	3
DOIs	https://doi.org/10.1109/18.490556
State	Published - 1996

Bibliographical note

Funding Information:
Manuscript received January 3, 1994; revised December 10, 1995. This work was supported by ONR under Grant N00014-93-1-0485. Some results of this paper were presented at the Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, November 1993. G. Zhou is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. G. B. Giannakis is with the Department of Electrical Engineering, University of Virginia, Charlottesville, VA 22903-2442 USA. Publisher Item Identifier S 0018-9448(96)02909-4.

Keywords

Asymptotic properties
Ergodicity
Frequency- and phase-coupled harmonics
Multiplicative noise
Polyspectra

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10.1109/18.490556

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abstract = "Polyspectral analysis of processes with mixed spectra is considered, and scaled polyperiodograms are introduced to clarify issues related to stalionarity, ergodicity, and suppression of additive stationary noise in harmonic retrieval problems. Spectral and polyspectral approaches are capable of retrieving (un)coupled harmonics, not only when the harmonics have constant amplitudes, but also when they are observed in nonzero mean multiplicative noise. Fourier series polyspectra and asymptotic properties of scaled polyperiodograms provide general tools for higher order analysis of time series with mixed spectra. A single record phase coupling detector is derived to obviate the assumption of independent multiple records required by existing methods. The novelties are illustrated by simulation examples.",

keywords = "Asymptotic properties, Ergodicity, Frequency- and phase-coupled harmonics, Multiplicative noise, Polyspectra",

author = "Guotong Zhou and Giannakis, {Georgios R.}",

note = "Funding Information: Manuscript received January 3, 1994; revised December 10, 1995. This work was supported by ONR under Grant N00014-93-1-0485. Some results of this paper were presented at the Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, November 1993. G. Zhou is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. G. B. Giannakis is with the Department of Electrical Engineering, University of Virginia, Charlottesville, VA 22903-2442 USA. Publisher Item Identifier S 0018-9448(96)02909-4.",

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AU - Zhou, Guotong

AU - Giannakis, Georgios R.

N1 - Funding Information: Manuscript received January 3, 1994; revised December 10, 1995. This work was supported by ONR under Grant N00014-93-1-0485. Some results of this paper were presented at the Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, November 1993. G. Zhou is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. G. B. Giannakis is with the Department of Electrical Engineering, University of Virginia, Charlottesville, VA 22903-2442 USA. Publisher Item Identifier S 0018-9448(96)02909-4.

PY - 1996

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N2 - Polyspectral analysis of processes with mixed spectra is considered, and scaled polyperiodograms are introduced to clarify issues related to stalionarity, ergodicity, and suppression of additive stationary noise in harmonic retrieval problems. Spectral and polyspectral approaches are capable of retrieving (un)coupled harmonics, not only when the harmonics have constant amplitudes, but also when they are observed in nonzero mean multiplicative noise. Fourier series polyspectra and asymptotic properties of scaled polyperiodograms provide general tools for higher order analysis of time series with mixed spectra. A single record phase coupling detector is derived to obviate the assumption of independent multiple records required by existing methods. The novelties are illustrated by simulation examples.

AB - Polyspectral analysis of processes with mixed spectra is considered, and scaled polyperiodograms are introduced to clarify issues related to stalionarity, ergodicity, and suppression of additive stationary noise in harmonic retrieval problems. Spectral and polyspectral approaches are capable of retrieving (un)coupled harmonics, not only when the harmonics have constant amplitudes, but also when they are observed in nonzero mean multiplicative noise. Fourier series polyspectra and asymptotic properties of scaled polyperiodograms provide general tools for higher order analysis of time series with mixed spectra. A single record phase coupling detector is derived to obviate the assumption of independent multiple records required by existing methods. The novelties are illustrated by simulation examples.

KW - Asymptotic properties

KW - Ergodicity

KW - Frequency- and phase-coupled harmonics

KW - Multiplicative noise

KW - Polyspectra

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Polyspectral analysis of mixed processes and coupled harmonics

Abstract

Bibliographical note

Keywords

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