Phase-Locking value (PLV) is used to measure phase synchrony of narrowband signals, therefore, it is able
to provide a measure of dynamic functional connectivity (DFC) of brain interactions. Currently used PLV
methods compute the convolution of the signal at the target frequency with a complex Gabor wavelet centered
at that frequency. The phase of this convolution is extracted for all time-bins over trials for a pair of neural
signals. These time-bins set a limit on the temporal resolution for PLV, hence, for DFC. Therefore, these
methods cannot provide a true DFC in a strict sense.
PLV is defined as the absolute value of the characteristic function of the difference of instantaneous phases
(IP) of two analytic signals evaluated at s = 1. It is a function of the time. For the narrowband signal in
the stationary Gaussian white noise, we investigated statistics of (i) its phase, (ii) the maximum likelihood
estimate of its phase, and (iii) the phase-lock loop (PLL) measurement of its phase, derived the analytic
form of the probability density function (pdf) of the difference of IP, and expressed this pdf in terms of
signal-to-noise ratio (SNR) of signals. PLV is finally given by analytic formulas in terms of SNRs of a pair
of neural signals under investigation.
In this new approach, SNR, hence PLV, is evaluated at any time instant over repeated trials. Thus, the
new approach can provide a true DFC via PLV. This paper presents detailed derivations of this approach
and results obtained by using simulations for magnetoencephalography (MEG) data.