TY - JOUR
T1 - Synchrosqueezed wavelet transforms
T2 - An empirical mode decomposition-like tool
AU - Daubechies, Ingrid
AU - Lu, Jianfeng
AU - Wu, Hau Tieng
N1 - Funding Information:
The authors are grateful to the Federal Highway Administration, which supported this research via FHWA grant DTFH61-08-C-00028. They also thank Prof. Norden Huang and Prof. Zhaohua Wu for many stimulating discussions and their generosity in sharing their code and insights. They also thank MD. Shu-Shya Hseu and Prof. Yu-Te Wu for providing the real medical signal. They thank the anonymous referees for useful suggestions of improving the presentation of the paper.
PY - 2011/3
Y1 - 2011/3
N2 - 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.
AB - 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.
KW - Empirical mode decomposition
KW - Synchrosqueezing
KW - Time-frequency analysis
KW - Wavelet
UR - http://www.scopus.com/inward/record.url?scp=78751584911&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78751584911&partnerID=8YFLogxK
U2 - 10.1016/j.acha.2010.08.002
DO - 10.1016/j.acha.2010.08.002
M3 - Article
AN - SCOPUS:78751584911
SN - 1063-5203
VL - 30
SP - 243
EP - 261
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 2
ER -