Estimating the mode of a phase distribution

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionResearchpeer-review

    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.

    LanguageEnglish
    Title of host publicationConference Record of the 41st Asilomar Conference on Signals, Systems and Computers, ACSSC
    EditorsMichael B. Matthews
    Place of PublicationPiscataway, NJ
    PublisherInstitute of Electrical and Electronics Engineers (IEEE)
    Pages587-591
    Number of pages5
    ISBN (Print)9781424421107
    DOIs
    Publication statusPublished - 2007
    Event41st Asilomar Conference on Signals, Systems and Computers, ACSSC - Pacific Grove, CA, United States
    Duration: 4 Nov 20077 Nov 2007

    Other

    Other41st Asilomar Conference on Signals, Systems and Computers, ACSSC
    CountryUnited States
    CityPacific Grove, CA
    Period4/11/077/11/07

    Fingerprint

    Random variables

    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 University’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 pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

    Cite this

    Quinn, B. G. (2007). Estimating the mode of a phase distribution. In M. B. Matthews (Ed.), Conference Record of the 41st Asilomar Conference on Signals, Systems and Computers, ACSSC (pp. 587-591). [4487281] Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ACSSC.2007.4487281
    Quinn, B. G. / Estimating the mode of a phase distribution. Conference Record of the 41st Asilomar Conference on Signals, Systems and Computers, ACSSC. editor / Michael B. Matthews. Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2007. pp. 587-591
    @inproceedings{330af09a535746fd9ecc54bfbe61745e,
    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.",
    author = "Quinn, {B. G.}",
    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}€™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 pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.",
    year = "2007",
    doi = "10.1109/ACSSC.2007.4487281",
    language = "English",
    isbn = "9781424421107",
    pages = "587--591",
    editor = "Matthews, {Michael B.}",
    booktitle = "Conference Record of the 41st Asilomar Conference on Signals, Systems and Computers, ACSSC",
    publisher = "Institute of Electrical and Electronics Engineers (IEEE)",
    address = "United States",

    }

    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 proceedingConference proceeding contributionResearchpeer-review

    TY - GEN

    T1 - Estimating the mode of a phase distribution

    AU - Quinn, B. G.

    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 University’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 pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

    PY - 2007

    Y1 - 2007

    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.

    UR - http://www.scopus.com/inward/record.url?scp=50249118578&partnerID=8YFLogxK

    U2 - 10.1109/ACSSC.2007.4487281

    DO - 10.1109/ACSSC.2007.4487281

    M3 - Conference proceeding contribution

    SN - 9781424421107

    SP - 587

    EP - 591

    BT - Conference Record of the 41st Asilomar Conference on Signals, Systems and Computers, ACSSC

    A2 - Matthews, Michael B.

    PB - Institute of Electrical and Electronics Engineers (IEEE)

    CY - Piscataway, NJ

    ER -

    Quinn BG. Estimating the mode of a phase distribution. In Matthews MB, editor, Conference Record of the 41st Asilomar Conference on Signals, Systems and Computers, ACSSC. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). 2007. p. 587-591. 4487281 https://doi.org/10.1109/ACSSC.2007.4487281