Analysis of Intrinsic Mode Functions: A PDE Approach
Analysis of Intrinsic Mode Functions: A PDE Approach
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DOI：
10.1109/lsp.2009.2038770
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发表时间：
2010-04-01
影响因子：
3.9
通讯作者：
Boudraa, A. O.
中科院分区：
文献类型：
--
作者：
Diop, El Hadji S.;Alexandre, R.;Boudraa, A. O.
经验模态分解是信号处理的有力工具。由于其原始算法，最近的工作有助于其理论框架。在此基础上，对它的理解和形式化提供了一些数学贡献。在本文中，所谓的本地平均值计算的方式，它允许使用微分包络。这个新的配方使我们证明，筛选过程的迭代很好地近似的偏微分方程（PDE）的分辨率。固有模态函数最初是以直观的方式定义的。在这里，一个数学表征的模式给出了所提出的偏微分方程为基础的方法。
The empirical mode decomposition is a powerful tool for signal processing. Because of its original algorithmic, recent works have contributed to its theoretical framework. Following these works, some mathematical contributions on its comprehension and formalism are provided. In this paper, the so called local mean is computed in such a way that it allows the use of differential calculus on envelopes. This new formulation makes us prove that iterations of the sifting process are well approximated by the resolution of partial differential equations (PDE). Intrinsic mode functions are originally defined in a intuitive way. Herein, a mathematical characterization of modes is given with the proposed PDE-based approach.