Empirical Mode Decomposition for Trivariate Signals

An extension of empirical mode decomposition (EMD) is proposed in order to make it suitable for operation on trivariate signals. Estimation of local mean envelope of the input signal, a critical step in EMD, is performed by taking projections along multiple directions in three-dimensional spaces using the rotation property of quaternions. The proposed algorithm thus extracts rotating components embedded within the signal and performs accurate time-frequency analysis, via the Hilbert–Huang transform. Simulations on synthetic trivariate point processes and real-world three-dimensional signals support the analysis.

I. Introduction

The empirical mode decomposition (EMD) algorithm has been designed for the time-frequency analysis of real-world signals [1]. It decomposes the signal in hand into a number of oscillatory modes called intrinsic mode functions (IMFs), so that the application of Hilbert transform to these intrinsic mode functions provides meaningful instantaneous frequency estimates [2]. The IMFs are obtained directly from the data with no a priori assumptions regarding the data nature, making EMD suitable for the analysis of nonlinear and nonstationary signals. The time-frequency analysis via EMD has found a wide range of applications in signal processing and related fields [3]–[5].