Hilbert-Huang transform and its applications / editors, Norden E. Huang, Samuel S. P. Shen San.

Format:

Book

Contributor:

Huang, Norden E. (Norden Eh), 1937- editor.

Shen, Samuel S., editor.

Series:

Interdisciplinary mathematical sciences ; Volume 16.

Interdisciplinary Mathematical Sciences ; Volume 16

Language:

English

Subjects (All):

Hilbert-Huang transform.

Decomposition (Mathematics).

Physical Description:

1 online resource (399 p.)

Edition:

2nd ed.

Place of Publication:

Singapore : World Scientific, 2014.

Language Note:

English

Summary:

This book is written for scientists and engineers who use HHT (Hilbert-Huang Transform) to analyze data from nonlinear and non-stationary processes. It can be treated as a HHT user manual and a source of reference for HHT applications. The book contains the basic principle and method of HHT and various application examples, ranging from the correction of satellite orbit drifting to detection of failure of highway bridges. The thirteen chapters of the first edition are based on the presentations made at a mini-symposium at the Society for Industrial and Applied Mathematics in 2003. Some outstan

Contents:

PREFACE; CONTENTS; CHAPTER 1 INTRODUCTION TO THE HILBERT-HUANG TRANSFORM AND ITS RELATED MATHEMATICAL PROBLEMS; 1.1. Introduction; 1.2. The Hilbert-Huang transform; 1.2.1. The empirical mode decomposition method (the sifting process); 1.2.2. The Hilbert spectral analysis; 1.3. Recent developments; 1.3.1. Normalized Hilbert transform; 1.3.2. Confidence limit; 1.3.3. Statistical significance of IMFs; 1.4. Mathematical problems related to the HHT; 1.4.1. Adaptive data-analysis methodology; 1.4.2. Nonlinear system identification

1.4.3. The prediction problem for nonstationary processes (the end effects of EMD)1.4.4. Spline problems (the best spline implementation for HHT, convergence and 2-D); 1.4.5. The optimization problem (the best IMF selection and uniqueness mode mixing); 1.4.6. Approximation problems (the Hilbert transform and quadrature); 1.4.7. Miscellaneous statistical questions concerning HHT; 1.5. Conclusion; References; CHAPTER 2 ENSEMBLE EMPIRICAL MODE DECOMPOSITION AND ITS MULTI-DIMENSIONAL EXTENSIONS; 2.1. Introduction; 2.2. The empirical mode decomposition

2.3. The ensemble empirical mode decomposition2.4. The multi-dimensional ensemble empirical mode decomposition; 2.5. Summary and discussions; Acknowledgments; References; CHAPTER 3 MULTIVARIATE EXTENSIONS OF EMPIRICAL MODE DECOMPOSITION; 3.1. Introduction; 3.2. Multivariate extensions of EMD; 3.2.1. Complex extensions of EMD; 3.2.1.1. Complex EMD (CEMD); 3.2.1.2. Rotation-invariant EMD; 3.2.1.3. Bivariate EMD; 3.2.1.4. Data-driven direction vectors in BEMD; 3.2.2. Trivariate EMD; 3.2.3. Multivariate EMD; 3.3. Mode-alignment property of MEMD

3.4. Filter bank property of MEMD and noise-assisted MEMD3.5. Applications; 3.5.1. Speed estimation using Doppler radar data; 3.5.2. Respiration study using NA-MEMD; 3.5.3. Classification of motor imagery data; 3.6. Discussion and conclusions; Referrence; CHAPTER 4 B-SPLINE BASED EMPIRICAL MODE DECOMPOSITION; 4.1. Introduction; 4.2. A B-spline algorithm for empirical mode decomposition; 4.3. Some related mathematical results; 4.4. Performance analysis of BS-EMD; 4.5. Application examples; 4.6. Conclusion and future research topics; Acknowledgements; References

CHAPTER 5 EMD EQUIVALENT FILTER BANKS, FROM INTERPRETATION TO APPLICATIONS5.1. Introduction; 5.2. A stochastic perspective in the frequency domain; 5.2.1. Model and simulations; 5.2.2. Equivalent transfer functions; 5.3. A deterministic perspective in the time domain; 5.3.1. Model and simulations; 5.3.2. Equivalent impulse responses; 5.4. Selected applications; 5.4.1. EMD-based estimation of scaling exponents; 5.4.2. EMD as a data-driven spectrum analyzer; 5.4.3. Denoising and detrending with EMD; 5.5. Concluding remarks; References; CHAPTER 6 HHT SIFTING AND FILTERING; 6.1. Introduction

6.2. Objectives of HHT sifting

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on print version record.

ISBN:

981-4508-24-1