A novel instantaneous phase difference estimator: piecewise maximum cross-correlation function

The instantaneous phase synchrony estimation of biomedical signals is of increasing concern in terms of revealing bivariate dynamics of biological systems. The estimation of phase synchronization contains two major parts: the phase difference estimation and the synchronization index calculation. In recent studies of cerebral autoregulation (CA), a number of instantaneous phase difference estimation methods have been proposed to study instantaneous dynamic between arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV). In this study, we took complex Morlet wavelet (CMW), the most widely used method as an example to discuss the possible limitations and propose a time-shift based method, piecewise maximum cross correlation function (PMCC) method. The analysis and the results show that PMCC avoids the trade-off between time and frequency resolution which exists in wavelet or short time Fourier transform based methods, and performs well in anti-noise. We finally discussed the limitation of PMCC.