A Time-Frequency-Based Approach to Phase and Phase Synchrony Estimation

Time-varying phase synchrony is an important bivariate measure that quantifies the dynamics between nonstationary signals and has been widely used in many applications including chaotic oscillators in physics and multichannel electroencephalography recordings in neuroscience. Current state-of-the-art in time-varying phase estimation uses either the Hilbert transform or the complex wavelet transform of the signals. Both of these methods have some major drawbacks such as the assumption that the signals are narrowband for the Hilbert transform and the nonuniform time-frequency resolution inherent to the wavelet analysis. In this paper, a new phase estimation method based on the Rihaczek distribution and Reduced Interference Rihaczek distribution belonging to Cohen's class is proposed. These distributions offer phase estimates with uniformly high time-frequency resolution which can be used for defining time and frequency dependent phase synchrony. Properties of the phase estimator and the corresponding phase synchrony measure are evaluated both analytically and through simulations showing the effectiveness of the new measures compared to existing methods.