A new nonlinear filter design for the detection of phase transitions in ECoG data

Understanding neocortical dynamics at mesoscopic level is an important area of experimental neuroscience. ECoG signals reveal us intercortical communications of neural populations in the form of spatial patterns appeared both in amplitude (AM) and phase (PM) modulation of gamma and beta waves. Neocortex shows multiple overlapping autonomous AM-PM phase transition patterns during cognitive processing. We propose an efficient digital filtering method for the capturing abrupt phase transitions defined in analytic phase domain. Phase transitions occurring on the surface of cortex can cover an area ranging from a few hypercolumns to the entire hemisphere. We develop an accurate and adaptable digital filter which is robust to variations in the bandpass filter characteristics and able to separate real transitions from artifacts caused by phase slips. We study complex polynomials which are derived from pseudo spectrum estimation of analytic signals reflecting the dynamics of grid topology. We classify the roots of this complex polynomial defined at each sample according to their location either outside or inside the unit disk in complex plane. The analysis of root characteristics enables us to identify phase transitions. The results are demonstrated using actual ECoG signals.