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The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

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TLDR
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...

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Efficient Heart Sound Segmentation and Extraction Using Ensemble Empirical Mode Decomposition and Kurtosis Features

TL;DR: An efficient heart sound segmentation method that automatically detects the location of first ( S1) and second ( S2) heart sound and extracts them from heart auscultatory raw data is presented here and paves the way for further exploitation of the diagnostic value of heart sounds in everyday clinical practice.
Journal ArticleDOI

2D Empirical Transforms. Wavelets, Ridgelets, and Curvelets Revisited

TL;DR: This paper revisits some well-known transforms of wavelet transform and shows that it is possible to build their empirical counterparts and proves that such constructions lead to different adaptive frames which show some promising properties for image analysis and processing.
Journal ArticleDOI

Quantitative diagnosis of a spall-like fault of a rolling element bearing by empirical mode decomposition and the approximate entropy method

TL;DR: In this article, the authors applied the approximate entropy (ApEn) method and empirical mode decomposition (EMD) to clearly separate the entry-exit events, and thus the size of the spall-like fault is estimated.
Journal ArticleDOI

Detecting anomalies in beams and plate based on the Hilbert Huang transform of real signals

TL;DR: In this paper, the feasibility of the Hilbert-Huang transform (HHT) as a signal processing tool for locating an anomaly, in the form of a crack, delamination, stiffness loss or boundary in beams and plate, based on physically acquired propagating wave signals.
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Research and application of improved adaptive MOMEDA fault diagnosis method

TL;DR: The article preprocesses the composite fault with ensemble empirical mode decomposition (EEMD) and then reconstructs the intrinsic mode function with the same time scale and proposes kurtosis spectral entropy as the objective function and uses the proposed method to search the complex fault pulse signals in strong noise environment.
References
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Journal ArticleDOI

Deterministic nonperiodic flow

TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Book

Linear and Nonlinear Waves

G. B. Whitham
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Book

RANDOM DATA Analysis and Measurement Procedures

TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.

Theory of communication

Dennis Gabor
Journal ArticleDOI

Mathematical analysis of random noise

TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
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