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Phase lag value/index (PLV/PLI)

HZ Hao Zhang
QZ Qing-Qi Zhou
HC He Chen
XH Xiao-Qing Hu
WL Wei-Guang Li
YB Yang Bai
JH Jun-Xia Han
YW Yao Wang
ZL Zhen-Hu Liang
DC Dan Chen
FC Feng-Yu Cong
JY Jia-Qing Yan
XL Xiao-Li Li
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PLV and PLI are commonly applied to acquire the strength of phase synchronization [110]. The instantaneous phase of signal x(t) is generated using the following formula:

Here, x~t signifies the Hilbert transform of xt, defined as follows:

PV refers to the Cauchy principal value. The PLV of two signals is defined as follows:

Here, Δt denotes the sampling period, N represents the number of samples per signal, j refers to the imaginary part, and e signifies the exponent. PLV signifies phase synchronization, with values ranging from 0 to 1. A value of 0 indicates a lack of synchronization, while 1 represents strict phase synchronization. On the other hand, PLI characterizes the asymmetry in the phase difference distribution between two signals. It is computed based on the relative phase difference between the two signals:

E represents expectation, the result value is located within the interval [0, 1], and a higher value indicates a higher phase synchronization.

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