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This thesis examines the empirical mode decomposition (EMD), a method fordecomposing multicomponent signals, from a modern, both theoretical andpractical, perspective. The motivation is to further formalize the concept anddevelop new methods to approach it numerically.  The theoretical part introduces a new formalization of the method as anoptimization problem over ordered function vector spaces. Using the theory of'convex-like' optimization and B-splines, Slater-regularity and thus strongduality of this optimization problem is shown. This results in a theoreticaljustification for the modern null-space-pursuit (NSP) operator-basedsignal-separation (OSS) EMD-approach for signal decomposition and spectralanalysis.  The practical part considers the identified strengths and weaknesses in OSSand NSP and proposes a hybrid EMD method that utilizes these modern, but alsoclassic, methods, implementing them in a toolbox called ETHOS (EMD Toolboxusing Hybrid Operator-Based Methods and B-splines) and applying them tocomparative examples. In the course of this part a new envelope estimationmethod called 'iterative slope envelope estimation' is proposed.

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