where and denote the discrete Fourier transforms of the two signals of interest x and y at frequency for the k-th EEG segment or epoch being the number of epochs. Re and Im denote the real and imaginary parts of a complex number c; denotes the modulus of c; and the superscript “*”, a complex conjugate. The instantaneous (zero-lag) connectivity component is closely related to the real part of the phase synchronization. Lagged phase synchronization, which statistically partials out the instantaneous component of the total connectivity, is defined as:
