Fast Multivariate Empirical Mode Decomposition

Abstract

The multivariate empirical mode decomposition (MEMD) has been pioneered recently for adaptively processing of multichannel data. Despite its high efficiency on time-frequency analysis of nonlinear and nonstationary signals, high computational load and over-decomposition have restricted wider applications of MEMD. To address these challenges, a fast MEMD (FMEMD) algorithm is proposed and featured by the following contributions: 1) A novel concept, pseudo direction-independent multivariate intrinsic mode function (IMIMF) which allows the interchange of sifting and projection operations, is defined for the purpose of developing FMEMD; 2) FMEMD is computationally efficient. Compared with MEMD, the number of time-consuming sifting operations reduces from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K \cdot p$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> for each iteration, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> denote the number of projection directions and signal dimension, respectively; 3) FMEMD is consistent with EMD in terms of the dyadic filter bank property; and 4) FMEMD is more effective in working at low sampling rate. Validity of the raised approach is demonstrated on a wide variety of real world applications.