Understanding dynamics of the system using Hilbert phases: an application to study neonatal and fetal brain signals

The Hilbert phase phi(t) of a signal x(t) exhibits slips when the magnitude of their successive phase difference |phi(t(i+1))-phi(t(i))| exceeds pi. By applying this approach to periodic, uncorrelated, and long-range correlated data, we show that the standard deviation of the time difference between the successive phase slips Deltatau normalized by the percentage of slips in the data is characteristic of the correlation in the data. We consider a 50x50 square lattice and model each lattice point by a second-order autoregressive (AR2) process. Further, we model a subregion of the lattice using a different set of AR2 parameters compared to the rest. By applying the proposed approach to the lattice model, we show that the two distinct parameter regions introduced in the lattice are clearly distinguishable. Finally, we demonstrate the application of this approach to spatiotemporal neonatal and fetal magnetoencephalography signals recorded using 151 superconducting quantum interference device sensors to identify the sensors containing the neonatal and fetal brain signals and discuss the improved performance of this approach over the traditionally used spectral approach.