Statistical Analysis of the Phase-Locking Value

The phase-locking value (PLV) is an important measure of synchronization when studying biosignals and especially electrical brain activities. Because the physical interpretation of the instantaneous phase of broadband signals leads to difficulties, most applications using the PLV deal with narrowband signals. The paper presents a statistical analysis of the PLV under the influence of Gaussian, Uniform and Laplace noise when added to the instantaneous phases and frequencies of mono- and two-component signals. We derive analytical expressions for the PLV values for these conditions and show that the PLV is rapidly dropping with increasing noise variance: broadening the frequency spectrum. We show that the noise influence on the instantaneous frequency is much more pronounced than on the instantaneous phase. We also introduce the concept of PLV-coherence time by analogy to optical coherence. Finally, we show that two signals with identical factitious instantaneous frequency as found in multicomponent signals can be phase locked leading to possible wrong interpretations of the PLV.