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This text describes a generalization of the analytic signal (Gabor, 1946)approach for the definition of instantaneous amplitude and phase to the case ofmultivariate signals. It was originally written as an appendix for anotherpaper, where the determination of the locally dominant oscillatory direction(the instantaneous amplitude) described here is used as a preprocessing stepfor another kind of data analysis. The text is reproduced in a 'standalone'form because the procedure might prove useful in other contexts too, especiallyfor the purpose of phase synchronization analysis (Rosenblum et al., 1996)between two (or more) multivariate sets of time series (Pascual-Marqui, 2007).

Instantaneous oscillatory direction and phase for multivariate timeseries