1EMD Revisited: A New Understanding of the Envelope and Resolving the Mode-Mixing Problem in AM-FM Signals

Empirical Mode Decomposition (EMD) is an adaptive and data-driven approach for analyzing multi-component nonlinear and non-stationary signals. The stop criterion, envelope technique, and mode-mixing problem are the most important topics that need to be addressed in order to improve the EMD algorithm. In this paper, we study the envelope technique and the mode-mixing problem caused by separating multicomponent AM-FM signals with the EMD algorithm. We present a new necessary condition on the envelope that questions the current assumption that the envelope passes through the extrema points of an intrinsic mode function (IMF). Then, we present a solution to the mode-mixing problem that occurs when multicomponent AM-FM signals are separated. We experiment on several signals, including simulated signals and real-life signals, to demonstrate the efficacy of the proposed method in resolving the mode-mixing problem. I