Empirical Mode Decomposition Algorithm: The 2007 Version by French Researchers

This article provides a detailed examination of the Empirical Mode Decomposition (EMD) algorithm originally proposed by French researchers. The focus is specifically on the 2007 release, which gained widespread adoption due to its effective handling of boundary conditions through mirror extension techniques. The algorithm's core methodology involves an iterative sifting process that decomposes nonlinear and non-stationary signals into intrinsic mode functions (IMFs) while satisfying two key conditions: (1) the number of extrema and zero-crossings must differ by at most one, and (2) the mean of the envelope defined by local maxima and minima must approach zero. While the 2007 version already delivered satisfactory results for many applications, subsequent developments have introduced enhancements like ensemble EMD (EEMD) and complete EEMD (CEEMD) to address mode mixing issues and improve stability. The implementation typically involves Hilbert-Huang transform components for instantaneous frequency analysis, making EMD particularly valuable for biomedical signal processing, seismic data analysis, and mechanical fault diagnosis applications. Despite being superseded by more advanced variants, this foundational version remains significant for its pioneering approach to adaptive time-frequency analysis.