Estimating the mode of a phase distribution

B. G. Quinn

doi:10.1109/ACSSC.2007.4487281

Estimating the mode of a phase distribution

B. G. Quinn

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

10 Citations (Scopus)

95 Downloads (Pure)

Abstract

If the phase of the theoretical mean of a complex-valued random variable is estimated by the sample mean of observed phases, there is a theoretical bias which results from the fact that phases are only measured on an interval of length 2π, so that, for example, -π and π may represent the same phase. Thus if a true phase or direction is say, near π, then the observed phases may instead be near - π. In this paper, a least squares estimator of phase is proposed which accounts for this "phase-wrapping". The estimator is shown to be strongly consistent and its central limit theorem is derived. The results of various simulations are described, for different values of sample size, SNR and theoretical phase. The technique and methods of analysis may prove useful in the more complicated estimation of frequency from the phases of a complex sinusoid.

Original language	English
Title of host publication	Conference Record of the 41st Asilomar Conference on Signals, Systems and Computers, ACSSC
Editors	Michael B. Matthews
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	587-591
Number of pages	5
ISBN (Print)	9781424421107
DOIs	https://doi.org/10.1109/ACSSC.2007.4487281
Publication status	Published - 2007
Event	41st Asilomar Conference on Signals, Systems and Computers, ACSSC - Pacific Grove, CA, United States Duration: 4 Nov 2007 → 7 Nov 2007

Other

Other	41st Asilomar Conference on Signals, Systems and Computers, ACSSC
Country/Territory	United States
City	Pacific Grove, CA
Period	4/11/07 → 7/11/07

Bibliographical note

Copyright 2007 IEEE. Reprinted from Conference record of the forty-first Asilomar conference on signals, systems and computers. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Macquarie Universityâ€™s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

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10.1109/ACSSC.2007.4487281

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Cite this

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title = "Estimating the mode of a phase distribution",

abstract = "If the phase of the theoretical mean of a complex-valued random variable is estimated by the sample mean of observed phases, there is a theoretical bias which results from the fact that phases are only measured on an interval of length 2π, so that, for example, -π and π may represent the same phase. Thus if a true phase or direction is say, near π, then the observed phases may instead be near - π. In this paper, a least squares estimator of phase is proposed which accounts for this {"}phase-wrapping{"}. The estimator is shown to be strongly consistent and its central limit theorem is derived. The results of various simulations are described, for different values of sample size, SNR and theoretical phase. The technique and methods of analysis may prove useful in the more complicated estimation of frequency from the phases of a complex sinusoid.",

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note = "Copyright 2007 IEEE. Reprinted from Conference record of the forty-first Asilomar conference on signals, systems and computers. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Macquarie University{\^a}€{\texttrademark}s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.; 41st Asilomar Conference on Signals, Systems and Computers, ACSSC ; Conference date: 04-11-2007 Through 07-11-2007",

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Quinn, BG 2007, Estimating the mode of a phase distribution. in MB Matthews (ed.), Conference Record of the 41st Asilomar Conference on Signals, Systems and Computers, ACSSC., 4487281, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 587-591, 41st Asilomar Conference on Signals, Systems and Computers, ACSSC, Pacific Grove, CA, United States, 4/11/07. https://doi.org/10.1109/ACSSC.2007.4487281

Estimating the mode of a phase distribution. / Quinn, B. G.
Conference Record of the 41st Asilomar Conference on Signals, Systems and Computers, ACSSC. ed. / Michael B. Matthews. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2007. p. 587-591 4487281.

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

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N1 - Copyright 2007 IEEE. Reprinted from Conference record of the forty-first Asilomar conference on signals, systems and computers. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Macquarie Universityâ€™s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

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N2 - If the phase of the theoretical mean of a complex-valued random variable is estimated by the sample mean of observed phases, there is a theoretical bias which results from the fact that phases are only measured on an interval of length 2π, so that, for example, -π and π may represent the same phase. Thus if a true phase or direction is say, near π, then the observed phases may instead be near - π. In this paper, a least squares estimator of phase is proposed which accounts for this "phase-wrapping". The estimator is shown to be strongly consistent and its central limit theorem is derived. The results of various simulations are described, for different values of sample size, SNR and theoretical phase. The technique and methods of analysis may prove useful in the more complicated estimation of frequency from the phases of a complex sinusoid.

AB - If the phase of the theoretical mean of a complex-valued random variable is estimated by the sample mean of observed phases, there is a theoretical bias which results from the fact that phases are only measured on an interval of length 2π, so that, for example, -π and π may represent the same phase. Thus if a true phase or direction is say, near π, then the observed phases may instead be near - π. In this paper, a least squares estimator of phase is proposed which accounts for this "phase-wrapping". The estimator is shown to be strongly consistent and its central limit theorem is derived. The results of various simulations are described, for different values of sample size, SNR and theoretical phase. The technique and methods of analysis may prove useful in the more complicated estimation of frequency from the phases of a complex sinusoid.

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Y2 - 4 November 2007 through 7 November 2007

ER -

Estimating the mode of a phase distribution

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