一种替代经验模态分解的前向偏微分方程方法
A Novel Foward-PDE Approach as an Alternative to Empirical Mode Decomposition
摘要：
本文提出了一种经验模态分解（EMD）的数学模型.经验模态分解虽然是信号处理的有力工具，但算法本身缺乏相应的理论基础。经验模态分解方法中涉及的插值和迭代过程一直是数学建模的障碍。在这里，我们提出了一种新的前向热方程的方法来表示平均包络和筛选过程。这种新的模型可以提供一个更好的数学分析的经典EMD以及识别其局限性。我们的方法实现了更好的性能相比，经典的EMD方法的“模式混合”的信号，是更强大的噪声。此外，我们还讨论了EMD分离信号的能力以及通过调整参数可能得到的改进。
英文摘要：
In this paper we present a mathematical model of the Empirical Mode Decomposition (EMD). Although EMD is a powerful tool for signal processing, the algorithm itself lacks an appropriate theoretical basis. The interpolation and iteration processes involved in the EMD method have been obstacles for mathematical modelling. Here, we propose a novel forward heat equation approach to represent the mean envelope and sifting process. This new model can provide a better mathematical analysis of classical EMD as well as identifying its limitations. Our approach achieves a better performance for a "mode-mixing" signal as compared to the classical EMD approach and is more robust to noise. Furthermore, we discuss the ability of EMD to separate signals and possible improvements by adjusting parameters.
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