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In this work, we present a new technique for the decomposition ofmultivariate data, which we call Multivariate Fast Iterative Filtering (MvFIF)algorithm. We study its properties, proving rigorously that it converges infinite time when applied to the decomposition of any kind of multivariatesignal.  We test MvFIF performance using a wide variety of artificial and realmultivariate signals, showing its ability to: separate multivariate modulatedoscillations; align frequencies along different channels; produce aquasi--dyadic filterbank when decomposing white Gaussian noise; decompose thesignal in a quasi--orthogonal set of components; being robust to noiseperturbation, even when the number of channels is increased considerably.  Finally, we compare its performance with the one of the main methodsdeveloped so far in the literature, proving that MvFIF produces, without any apriori assumption on the signal under investigation and in a fast and reliablemanner, a uniquely defined decomposition of any multivariate signal.

Multivariate Fast Iterative Filtering for the decomposition of nonstationary signals