Phase locking value (PLV) between $x(t)$ and $x(t-T)$ I have been trying to calculate PLV using the hilbert transform (reference). To test if it even works or not, I calculated PLV between $x(t)$ and $x(t-T)$. i find that it drops to zero very quickly as $T$ becomes nonzero as shown in following figure:


Is this as expected? I would expect PLV between $x(t)$ and $x(t-T)$ to be 1. In above graph shift is a normalized quantity such that $T=\rm{shift}\times\rm{length}(x)$

EDIT: thinking about this some more. Let us first define what PLV is. If we define PLV as the phase locking between instantaneous phases of two signals $x(t)$ and $y(t)$ where instantaneous phase is defined according to the analytic signal, then I am not able to derive a mathematical relationship asserting that $PLV(x(t),x(t-T)) = 1$. But then what is the PLV good for? What kind of transformation could be applied to $x(t)$ to yield a $y(t)$ s.t. $PLV(x,y)=1$?
PLV is good for correlating signals that seem out of phase to our measurement techniques due to the digital nature of our recordings but are in sync because of the electro chemical biological nature of the CNS. If you transform two signals into phase you can determine the relatedness of the two signals.

Phase Locking Value NeuroBytes
The schematic below illustrates how PLV is computed in this implementation. Explanation for each step follows.