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.

翻译：本论文从现代理论与实际应用的双重视角，系统研究了用于多分量信号分解的经验模态分解（EMD）方法。研究旨在进一步形式化该概念，并开发新的数值求解方法。理论部分提出了一种新的形式化框架，将EMD视为在有序函数向量空间上的优化问题。通过运用"类凸"优化理论与B样条方法，证明了该优化问题的Slater正则性及强对偶性，从而为基于现代零空间追踪（NSP）算子的信号分离（OSS）EMD方法在信号分解与谱分析中的应用提供了理论依据。实践部分分析了OSS与NSP方法的优缺点，提出了一种融合现代方法与经典技术的混合EMD方法，并将其实现为名为ETHOS（基于混合算子方法与B样条的EMD工具箱）的工具包，通过对比实例验证其性能。在此过程中，还提出了一种名为"迭代斜率包络估计"的新型包络估计方法。