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Neural Comput. 2013 Apr;25(4):901-21. doi: 10.1162/NECO_a_00422. Epub 2013 Jan 22.

Some sampling properties of common phase estimators.

Author information

1
Department of Mathematics, Boston University, Boston, MA 02446, USA. lepage@math.bu.edu

Abstract

The instantaneous phase of neural rhythms is important to many neuroscience-related studies. In this letter, we show that the statistical sampling properties of three instantaneous phase estimators commonly employed to analyze neuroscience data share common features, allowing an analytical investigation into their behavior. These three phase estimators-the Hilbert, complex Morlet, and discrete Fourier transform-are each shown to maximize the likelihood of the data, assuming the observation of different neural signals. This connection, explored with the use of a geometric argument, is used to describe the bias and variance properties of each of the phase estimators, their temporal dependence, and the effect of model misspecification. This analysis suggests how prior knowledge about a rhythmic signal can be used to improve the accuracy of phase estimates.

PMID:
23339610
PMCID:
PMC3596472
DOI:
10.1162/NECO_a_00422
[Indexed for MEDLINE]
Free PMC Article
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