Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool
Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool
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DOI：
10.1016/j.acha.2010.08.002
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发表时间：
2011-03-01
影响因子：
2.5
通讯作者：
Wu, Hau-Tieng
中科院分区：
文献类型：
--
作者：
Daubechies, Ingrid;Lu, Jianfeng;Wu, Hau-Tieng
EMD 算法是一种旨在将函数分解为其构建块的技术，这些函数是（相当）少量分量的叠加，在时频平面上很好地分离，每个分量都可以被视为局部近似谐波，具有缓慢变化的幅度和频率。 EMD 已经在气象学、结构稳定性分析、医学研究等广泛应用中显示出其实用性。另一方面，EMD 算法包含启发式和临时元素，这使得数学分析变得困难。在本文中，我们描述了一种捕捉 EMD 方法的风格和原理的方法，尽管在构建组件时使用了不同的方法。所提出的方法是小波分析和重新分配方法的结合。我们为一类函数引入了精确的数学定义，这些函数可以被视为相当少量的近似谐波分量的叠加，并且我们证明我们的方法确实成功地分解了此类中的任意函数。我们提供了几个模拟数据和真实数据的示例。 (C) 2010 Elsevier Inc. 保留所有权利。
The EMD algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of components, well separated in the time-frequency plane, each of which can be viewed as approximately harmonic locally, with slowly varying amplitudes and frequencies. The EMD has already shown its usefulness in a wide range of applications including meteorology, structural stability analysis, medical studies. On the other hand, the EMD algorithm contains heuristic and ad hoc elements that make it hard to analyze mathematically.In this paper we describe a method that captures the flavor and philosophy of the EMD approach, albeit using a different approach in constructing the components. The proposed method is a combination of wavelet analysis and reallocation method. We introduce a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and we prove that our method does indeed succeed in decomposing arbitrary functions in this class. We provide several examples, for simulated as well as real data. (C) 2010 Elsevier Inc. All rights reserved.