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