To investigate movement-related PAC, both by comparing it under different conditions and by tracking its dynamics over a movement cycle, we applied time-resolved PAC analysis. The source signals (i.e., component time courses) were first filtered into β (13–30 Hz) and γ (50–150 Hz) bands. The width of γ frequency was defined based on previous literature (9, 14). Subsequently, the Hilbert transform was applied to extract the phase of the β band and the amplitude of the γ band. Then, for each 3 s epoch in a component, we computed PAC in successive windows (300 ms, corresponding to 4–10 cycles for the β activities) shifted by 50 ms time steps. We applied the normalized mean vector length (MVL) method (34, 35), in which the normalization factor is the square root mean of the γ amplitudes in a time window. As the time window was rather short, which might lead to inaccurate PAC estimation, the z-score of the MVL (zMVL) was calculated using the mean and standard deviation of 200 surrogates, created by recombining the instantaneous phase and randomized shuffled amplitudes. zMVL
