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

AN - SCOPUS:50249118578

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

T2 - 41st Asilomar Conference on Signals, Systems and Computers, ACSSC

Y2 - 4 November 2007 through 7 November 2007

ER -