Topic
Hilbert spectral analysis
About: Hilbert spectral analysis is a research topic. Over the lifetime, 1505 publications have been published within this topic receiving 54482 citations.
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TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...
18,956 citations
Book•
01 Jan 1993
TL;DR: In this article, the main properties of bounded and unbounded operators, adjoint operators, symmetric and self-adjoint operators in hilbert spaces are discussed, as well as the stability of self-jointness under small perturbations.
Abstract: linear operators in hilbert spaces | springerlink abstract. we recall some fundamental notions of the theory of linear operators in hilbert spaces which are required for a rigorous formulation of the rules of quantum mechanics in the one-body case. in particular, we introduce and discuss the main properties of bounded and unbounded operators, adjoint operators, symmetric and self-adjoint operators, self-adjointness criterion and stability of self-adjointness under small perturbations, spectrum, isometric and unitary operators, spectral
2,282 citations
TL;DR: In this paper, Hilbert spectral analysis is proposed as an alternative to wavelet analysis, which provides not only a more precise definition of particular events in time-frequency space, but also more physically meaningful interpretations of the underlying dynamic processes.
Abstract: We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.
1,945 citations
1,815 citations
TL;DR: Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research.
Abstract: [1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.
1,533 citations