Math @ Duke

Publications [#243764] of Jianfeng Lu
Papers Published
 Daubechies, I; Lu, J; Wu, HT, Synchrosqueezed wavelet transforms: An empirical mode decompositionlike tool,
Applied and Computational Harmonic Analysis, vol. 30 no. 2
(2011),
pp. 243261, Elsevier BV, ISSN 10635203 [doi]
(last updated on 2019/02/18)
Abstract: The EMD algorithm, first proposed in [11], made more robust as well as more
versatile in [12], 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 timefrequency 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  see, e.g. [13]. On the other hand, the EMD algorithm contains
heuristic and adhoc 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.
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.


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