Modern Methods for Signal Analysis: Empirical Mode Decomposition Theory and Hybrid Operator-Based Methods Using B-Splines (2302.03334v1)

Abstract: This thesis examines the empirical mode decomposition (EMD), a method for decomposing multicomponent signals, from a modern, both theoretical and practical, perspective. The motivation is to further formalize the concept and develop new methods to approach it numerically. The theoretical part introduces a new formalization of the method as an optimization problem over ordered function vector spaces. Using the theory of 'convex-like' optimization and B-splines, Slater-regularity and thus strong duality of this optimization problem is shown. This results in a theoretical justification for the modern null-space-pursuit (NSP) operator-based signal-separation (OSS) EMD-approach for signal decomposition and spectral analysis. The practical part considers the identified strengths and weaknesses in OSS and NSP and proposes a hybrid EMD method that utilizes these modern, but also classic, methods, implementing them in a toolbox called ETHOS (EMD Toolbox using Hybrid Operator-Based Methods and B-splines) and applying them to comparative examples. In the course of this part a new envelope estimation method called 'iterative slope envelope estimation' is proposed.