Towards a proper estimation of phase synchronization from time series

Area of Science:

• Signal Processing
• Neuroscience
• Complex Systems Analysis

Background:

• Estimating instantaneous amplitude and phase from scalar time series is crucial for synchronization studies.
• The complex plane representation is a common method for obtaining these signal characteristics [A(t), phi(t)].
• However, not all derived [A(t), phi(t)] pairs accurately represent the signal's true amplitude and phase.

Purpose of the Study:

• To define criteria for valid instantaneous amplitude and phase estimation.
• To identify limitations of the complex plane method for signals with complex spectral properties.
• To provide a practical method for assessing narrow-band behavior in time series data.

Main Methods:

• Theoretical analysis of complex plane representation for signal decomposition.
• Development of criteria for unambiguous amplitude-phase pair identification.
• Illustrative examples using simulated and real-world data (epileptic patient EEG).

Main Results:

• The complex plane representation can fail for multi-component or broadband signals.
• Criteria are established for ensuring the derived [A(t), phi(t)] pair is a valid representation.
• A practical procedure is presented to test for narrow-band signal characteristics.

Conclusions:

• Accurate instantaneous amplitude and phase estimation requires adherence to specific criteria.
• The complex plane method has limitations that must be recognized, especially for non-narrowband signals.
• Understanding these limitations is vital for reliable analysis of phase interdependencies and brain activity.