where the argument of the exponential function contains the phase difference between signals i and j, i.e., Δθij(f) = θi(f) − θj(f) ∈ [−π, π]. It turns out that coherence is the absolute value of the weighted average of eι Δθij(f) across signal realizations, where the weights are a function of the amplitudes. If the signals are independent, the phase difference varies randomly across realizations and the coherence vanishes. If the signals are phase-coupled, the phase difference fluctuates around some constant value, and the coherence is non-vanishing.
