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. $PLV(x,y)=1$?
Phase locking value (PLV) between $x(t)$ and $x(t-T)$
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