  Defining and measuring phase synchronization in a pair of nonlinear time
series are highly nontrivial. This can be done with the help of Fourier
transform, when it exists, for a pair of stored (hence stationary) signals. In
a time series instantaneous phase is often defined with the help of Hilbert
transform. In this paper phase of a time series has been defined with the help
of Fourier transform. This gives rise to a deterministic method to detect phase
synchronization in its most general form between a pair of time series. Since
this is a stricter method than the statistical methods based on instantaneous
phase, this can be used for lateralization and source localization of epileptic
seizures with greater accuracy. Based on this method a novel measure of phase
synchronization, called syn function, has been defined, which is capable of
quantifying neural phase synchronization and asynchronization as important
parameters of epileptic seizure dynamics. It has been shown that such a strict
measure of phase synchronization has potential application in seizure focus
localization from scalp electroencephalogram (EEG) data, without any knowledge
of electrical conductivity of the head.
