### 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.

Language | English |
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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 | |

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 |
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Country | United States |

City | Pacific Grove, CA |

Period | 4/11/07 → 7/11/07 |

### Fingerprint

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

*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

}

*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.

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