where df is an incremental step in the frequency domain, and F denotes the frequency band of interest. PSI is essentially a weighted average of the slope of the phase difference Δθij(f + df) − Δθij(f) across F, whose sign provides a measure of the directionality. In particular, a positive value indicates that the signal i precedes (thus leads) the signal j, while a negative value indicates the opposite (Basti et al., 2017). Similarly to ImCoh, PSI requires a phase slope between signals to be non-vanishing, and thus it does not lead to artifactual detection of directed connectivity due to artificial zero-lag correlations.
