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Unified framework for detecting phase synchronization in coupled time series.

Junfeng Sun1, Michael Small

  • 1Med-X Research Institute, Shanghai Jiao Tong University, Shanghai, China. jfsun@sjtu.edu.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

This study unifies instantaneous phase (IP) definitions for analyzing phase synchronization (PS) in bivariate time series. Noise in IP estimation degrades mean phase coherence, with degradation dependent on in-band noise levels.

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Area of Science:

  • Signal Processing
  • Circular Statistics
  • Time Series Analysis

Background:

  • Phase synchronization (PS) is crucial for analyzing coupled systems.
  • Existing methods for detecting PS in bivariate time series have limitations.
  • Understanding instantaneous phase (IP) is key to accurate PS detection.

Purpose of the Study:

  • To unify definitions of instantaneous phase (IP) within a signal processing framework.
  • To investigate the impact of noise on IP estimation and its effect on PS detection.
  • To provide a theoretical basis for understanding PS in noisy bivariate time series.

Main Methods:

  • Revisiting and unifying multiple instantaneous phase (IP) definitions.
  • Developing a framework defining IP as the argument of a bandpass-filtered signal.
  • Analyzing the statistical properties of IP estimation errors due to noise, identifying them as scale mixture of normal (SMN) distributions.
  • Approximating SMN distributions with normal distributions to analyze coherence degradation.

Main Results:

  • A unified framework for IP definition is established.
  • IP estimation errors are shown to follow scale mixture of normal (SMN) distributions.
  • Mean phase coherence in bivariate time series is degraded by a factor directly related to in-band noise levels.
  • Theoretical results are validated through simulations.

Conclusions:

  • The unified IP framework clarifies constraints and noise effects in PS analysis.
  • Noise-induced errors in IP estimation have a quantifiable impact on mean phase coherence.
  • The findings offer a deeper understanding of phase synchronization detection in noisy bivariate time series.