Quantifying coevolution of nonstationary biomedical signals using time-varying phase spectra

We present a novel time-varying phase spectrum (TVPS) method to quantify the dynamics of coevolution of two persistent nonstationary coupled signals. Based on the TVPS, an instantaneous intersignal phase shift is defined within the primary frequency range in which the two signals are highly correlated. The TVPS is estimated using a fixed-window method or an adaptive-window method. In the latter method, the window length changes dynamically and automatically as a function of change in frequency of the signals. The effects of altering window types and lengths on the accuracy of the estimation of the primary phase shift is assessed by analyzing synthesized linear chirp signals with decaying amplitude and constant relative phase shift or decaying amplitude and changing relative phase shifts. The methods developed are also used for determining the evolution of the primary phase shift among ventral root activities during fictive locomotion in an in vitro rat spinal cord preparation. The analyses indicate that the TVPS method in conjunction with the determination of the primary frequency range, allows determination of both the evolution of the coupling strength and the evolution of the phase shift between two persistent nonstationary rhythmic signals in the joint time-frequency domain. An adaptive window reduces the estimation bias and the estimation variability.