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Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. (English) Zbl 1213.42133

The EMD (Empirical Mode Decomposition) algorithm decomposes a signal into a superposition of a reasonably small number of well separated components in the time-frequency plane. The EMD algorithm has demonstrated many interesting applications for a wide range of applications. However, it contains heuristic and ad hoc elements that make it hard to analyze mathematically. The main goal of this paper is to propose an equally effective EMD-like algorithm using synchrosqueezed wavelet transforms, and then to provide a rigorous mathematical analysis for it. The synchrosqueezed wavelet transforms are described in section 2. The authors propose an empirical mode decomposition-like tool which shares the same philosophy and spirit of EMD. In Theorem 3.3, the authors provide a satisfactory mathematical analysis of the proposed method for the class of functions in \(\mathcal{A}_{\epsilon,d}\) which is defined in Definition 3.2 and uses the IMT (Intrinsic Mode Type function) in Definition 3.1. Many convincing numerical examples are given in section 5 to demonstrate the effectiveness of the proposed method for synthesized data and real data. This paper makes a significant contribution in the understanding of EMD algorithm.
Reviewer: Bin Han (Edmonton)

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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