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Coherence and phase synchronization between time series corresponding todifferent spatial locations are usually interpreted as indicators of theconnectivity between locations. In neurophysiology, time series of electricneuronal activity are essential for studying brain interconnectivity. Suchsignals can either be invasively measured from depth electrodes, or computedfrom very high time resolution, non-invasive, extracranial recordings of scalpelectric potential differences (EEG: electroencephalogram) and magnetic fields(MEG: magnetoencephalogram) by means of a tomography such as sLORETA(standardized low resolution brain electromagnetic tomography). There are twoproblems in this case. First, in the usual situation of unknown corticalgeometry, the estimated signal at each brain location is a vector with threecomponents (i.e. a current density vector), which means that coherence andphase synchronization must be generalized to pairs of multivariate time series.Second, the inherent low spatial resolution of the EEG/MEG tomographyintroduces artificially high zero-lag coherence and phase synchronization. Inthis report, solutions to both problems are presented. Two additionalgeneralizations are briefly mentioned: (1) conditional coherence and phasesynchronization; and (2) non-stationary time-frequency analysis. Finally, anon-parametric randomization method for connectivity significance testing isoutlined. The new connectivity measures proposed here can be applied to pairsof univariate EEG/MEG signals, as is traditional in the published literature.However, these calculations cannot be interpreted as connectivity, since it isin general incorrect to associate an extracranial electrode or sensor to theunderlying cortex.

Coherence and phase synchronization: generalization to pairs of multivariate time series, and removal of zero-lag contributions