Multi-spectral phase coherence

Multi-spectral phase coherence (MSPC) is a generalized cross-frequency coupling metric introduced by Yang and colleagues in 2016. MSPC can be used to quantify nonlinear phase coupling between a set of base frequencies and their harmonic/intermodulation frequencies. MSPC is a model-free method, which can provide a system description, including (i) the order of the nonlinearity, (ii) the direction of interaction, (iii) the time delay in the system, and both (iv) harmonic and (v) intermodulation coupling.
The MSPC is defined as:
where formula_2 is the phase at frequency formula_3, formula_4 is the weight of formula_3 to a harmonic/intermodulation frequency formula_6), and formula_7 represents the average over realizations.
Bi-phase locking value, also called bi-phase coherence in the literature, is a special case of MSPC when formula_8, formula_9
The time-delay can be estimated from the phase lag when MSPC is computed between signals.