Quadrivariate Empirical Mode Decomposition

We introduce a quadrivariate extension of Empirical Mode Decomposition (EMD) algorithm, termed QEMD, as a tool for the time-frequency analysis of nonlinear and non-stationary signals consisting of up to four channels. The local mean estimation of the quadrivariate signal is based on taking real-valued projections of the input in different directions in a multidimensional space where the signal resides. To this end, the set of direction vectors is generated on 3-sphere (residing in 4D space) via the low-discrepancy Hammersley sequence. It has also been shown that the resulting set of vectors is more uniformly distributed on a 3-sphere as compared to that generated by a uniform angular coordinate system. The ability of QEMD to extract common modes within multichannel data is demonstrated by simulations on both synthetic and real-world signals.