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The Illustrated Wavelet Transform Handbook 2th 2016.pdf

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    Contents
    Chapter 1 ▪ Getting Started
    1.1 INTRODUCTION
    1.2 WAVELET TRANSFORM
    1.3 READING THE BOOK
    Chapter 2 ▪ The Continuous Wavelet Transform
    2.1 INTRODUCTION
    2.2 THE WAVELET
    2.3 REQUIREMENTS FOR THE WAVELET
    2.4 THE ENERGY SPECTRUM OF THE WAVELET
    2.5 WAVELET TRANSFORM
    2.6 IDENTIFICATION OF COHERENT STRUCTURES
    2.7 EDGE DETECTION
    2.8 INVERSE WAVELET TRANSFORM
    2.9 SIGNAL ENERGY: WAVELET-BASED ENERGY AND POWER SPECTRA
    2.10 WAVELET TRANSFORM IN TERMS OF THE FOURIER TRANSFORM
    2.11 COMPLEX WAVELETS: THE MORLET WAVELET
    2.12 WAVELET TRANSFORM, SHORT-TIME FOURIER TRANSFORM AND HEISENBERG BOXES
    2.13 ADAPTIVE TRANSFORMS: MATCHING PURSUITS
    2.14 WAVELETS IN TWO OR MORE DIMENSIONS
    2.15 THE CWT: COMPUTATION, BOUNDARY EFFECTS AND VIEWING
    2.16 RIDGE FOLLOWING AND SECONDARY WAVELET FEATURE DECOUPLING
    2.17 RIDGE HEIGHTS
    2.18 RUNNING WAVELET ARCHETYPING
    2.19 WAVELET TRANSFORM REPHASING
    2.20 REASSIGNMENT AND SYNCHROSQUEEZING
    2.21 COMPARING TWO SIGNALS USING WAVELET TRANSFORMS
    2.21.1 Transform Differences and Ratios
    2.21.2 Cross-Wavelet Transform
    2.21.3 Wavelet Cross-Correlation
    2.21.4 Phase Comparison Measures
    2.21.5 Wavelet Coherence
    2.22 BICOHERENCE AND CROSS-BICOHERENCE
    2.23 ENDNOTES
    2.23.1 Chapter Key Words and Phrases
    2.23.2 Additional Notes and Resources
    2.23.3 Tings to Try
    2.23.4 Final Note: Te CWT as a ‘Sof Tool’ for Algorithm Development
    Chapter 3 ▪ The Discrete Wavelet Transform
    3.1 INTRODUCTION
    3.2 FRAMES AND ORTHOGONAL WAVELET BASES
    3.2.1 Frames
    3.2.2 Dyadic Grid Scaling and Orthonormal Wavelet Transforms
    3.2.3 Scaling Function and Multiresolution Representation
    3.2.4 Scaling Equation, Scaling Coefcients and Associated Wavelet Equation
    3.2.5 Haar Wavelet
    3.2.6 Coefcients from Coefcients: Fast Wavelet Transform
    3.3 DISCRETE INPUT SIGNALS OF FINITE LENGTH
    3.3.1 Approximations and Details
    3.3.2 Multiresolution Algorithm: An Example
    3.3.3 Wavelet Energy
    3.3.4 Alternative Indexing of Dyadic Grid Coefcients
    3.3.5 A Simple Worked Example: Te Haar Wavelet Transform
    3.4 EVERYTHING DISCRETE
    3.4.1 Discrete Experimental Input Signals
    3.4.2 Smoothing, Tresholding and Denoising
    3.5 DAUBECHIES WAVELETS
    3.5.1 Filtering
    3.5.2 Symmlets and Coiflets
    3.6 TRANSLATION INVARIANCE
    3.7 BIORTHOGONAL WAVELETS
    3.8 TWO-DIMENSIONAL WAVELET TRANSFORMS
    3.9 ADAPTIVE TRANSFORMS: WAVELET PACKETS
    3.10 ‘X-LETS’: CONTOURLETS, RIDGELETS, CURVELETS, SHEARLETS AND SO ON
    3.11 ENDNOTES
    3.11.1 Chapter Key Words and Phrases
    3.11.2 Further Resources
    Chapter 4 ▪ Fluids
    4.1 INTRODUCTION
    4.2 STATISTICAL MEASURES FOR FLUID TURBULENCE
    4.2.1 Moments, Energy and Power Spectra
    4.2.2 Intermittency and Correlation
    4.2.3 Wavelet Tresholding
    4.2.4 Wavelet Selection Using Entropy Measures
    4.3 ENGINEERING FLOWS
    4.3.1 Experimental Flows: Jets, Wakes, Turbulence and Coherent Structures
    4.3.2 Computational Fluid Dynamics: Simulation and Analysis
    4.3.3 Fluid–Structure Interaction
    4.4 GEOPHYSICAL FLOWS
    4.4.1 Atmospheric Processes: Wind, Boundary Layers and Turbulence
    4.4.2 Ocean Processes: Waves, Large-Scale Oscillations, Ocean–Atmosphere Interactions and Biological Processes
    4.4.3 Rainfall and River Flows
    4.5 TWO-PHASE FLOWS
    4.6 OTHER APPLICATIONS IN FLUIDS
    Chapter 5 ▪ Engineering Testing, Monitoring and Characterization
    5.1 INTRODUCTION
    5.2 DYNAMICS
    5.2.1 Fundamental Behaviour
    5.2.2 Chaos
    5.3 NON-DESTRUCTIVE TESTING OF STRUCTURAL ELEMENTS
    5.4 CONDITION MONITORING OF ROTATING MACHINERY
    5.4.1 Gears
    5.4.2 Shafs, Bearings and Blades
    5.5 MACHINING PROCESSES
    5.6 CHARACTERIZATION OF SURFACES AND FIBROUS MATERIALS
    5.7 OTHER APPLICATIONS IN ENGINEERING
    5.7.1 Compression
    5.7.2 Control
    5.7.3 Electrical Systems and Circuits
    5.7.4 Miscellaneous
    Chapter 6 ▪ Medicine
    6.1 INTRODUCTION
    6.2 ELECTROCARDIOGRAM
    6.2.1 ECG Beat Detection and Timings
    6.2.2 Detection of Abnormalities
    6.2.3 Heart Rate Variability
    6.2.4 Cardiac Arrhythmias
    6.2.5 ECG Data Compression
    6.2.6 Hardware Implementation
    6.3 NEUROELECTRIC WAVEFORMS
    6.3.1 Evoked Potentials and Event-Related Potentials
    6.3.2 Epileptic Seizures and Epileptogenic Foci
    6.3.3 Sleep Studies
    6.3.4 Other Areas
    6.4 PHOTOPLETHYSMOGRAM
    6.4.1 Respiratory Modulations, Respiratory Rate and Respiratory Effort
    6.4.2 Oxygen Saturation
    6.4.3 Te Video Photoplethysmogram (Video-PPG)
    6.4.4 Other Areas
    6.5 PATHOLOGICAL SOUNDS, ULTRASOUNDS AND VIBRATIONS
    6.5.1 Cardiovascular System
    6.5.2 Lung Sounds, Swallowing, Snoring and Speech
    6.5.3 Acoustic Response
    6.6 BLOOD FLOW AND BLOOD PRESSURE
    6.7 MEDICAL IMAGING
    6.7.1 Optical Imaging
    6.7.2 Ultrasonic Images
    6.7.3 Computed Tomography, Magnetic Resonance Imaging and Other Radiographic Images
    6.8 OTHER APPLICATIONS IN MEDICINE
    6.8.1 Electromyographic Signals
    6.8.2 Posture, Gait and Activity
    6.8.3 Analysis of Multiple Biosignals
    6.8.4 Miscellaneous
    Chapter 7 ▪ Fractals, Finance, Geophysics, Astronomy and Other Areas
    7.1 INTRODUCTION
    7.2 FRACTALS
    7.2.1 Exactly Self-Similar Fractals
    7.2.2 Stochastic Fractals
    7.2.3 Multifractals
    7.3 FINANCE
    7.4 GEOPHYSICS
    7.4.1 Properties of Subsurface Media: Well Logging, Cores and Seismic Methods
    7.4.2 Remote Sensing
    7.5 ASTRONOMY: SIGNALS AND IMAGES
    7.6 OTHER AREAS
    REFERENCES,
    APPENDIX: USEFUL BOOKS, PAPERS AND WEBSITES,
    INDEX,
    The Illustrated Wavelet Transform HandbookSECOND EDITIONIntroductory Theory and Applications in Science, Engineering, Medicine and Finance
    The Illustrated Wavelet Transform HandbookSECOND EDITIONPaul S. AddisonEdinburgh, ScotlandIntroductory Theory and Applications in Science, Engineering, Medicine and FinanceBoca Raton London New YorkCRC Press is an imprint of theTaylor & Francis Group, an informa business
    CRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742© 2017 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa businessNo claim to original U.S. Government worksPrinted on acid-free paperVersion Date: 20160621International Standard Book Number-13: 978-1-4822-5132-6 (paperback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint.Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers.For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copy-right.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.Library of Congress Cataloging‑in‑Publication DataNames: Addison, Paul S., author.Title: The illustrated wavelet transform handbook : introductory theory and applications in science, engineering, medicine and finance / Paul S. Addison.Description: Second edition. | Boca Raton, FL : CRC Press, Taylor & Francis Group, [2016] | Includes bibliographical references and index.Identifiers: LCCN 2016033578| ISBN 9781482251326 (hardback ; alk. paper) | ISBN 1482251329 (hardback ; alk. paper) | ISBN 9781482251333 (e-book) | ISBN 1482251337 (e-book)Subjects: LCSH: Wavelets (Mathematics) | Fourier analysis. | Biomedical engineering.Classification: LCC QA403.3 .A35 2016 | DDC 515/.2433--dc23LC record available at https://lccn.loc.gov/2016033578Visit the Taylor & Francis Web site athttp://www.taylorandfrancis.comand the CRC Press Web site athttp://www.crcpress.com
    To Hannah, Stephen, Anthony, Michael and, this time, David; to my dear parents, Josephine and Stanley, gone but still with us; and to my loving wife, Stephanie.Thank you.
    viiContentsPreface to Second Edition, xiiiPreface to First Edition, xvChapter 1 ▪ Getting Started 11.1 INTRODUCTION 11.2 WAVELET TRANSFORM 21.3 READING THE BOOK 4Chapter 2 ▪ The Continuous Wavelet Transform 72.1 INTRODUCTION 72.2 THE WAVELET 72.3 REQUIREMENTS FOR THE WAVELET 102.4 THE ENERGY SPECTRUM OF THE WAVELET 102.5 WAVELET TRANSFORM 122.6 IDENTIFICATION OF COHERENT STRUCTURES 142.7 EDGE DETECTION 222.8 INVERSE WAVELET TRANSFORM 242.9 SIGNAL ENERGY: WAVELET-BASED ENERGY AND POWER SPECTRA 282.10 WAVELET TRANSFORM IN TERMS OF THE FOURIER TRANSFORM 332.11 COMPLEX WAVELETS: THE MORLET WAVELET 342.12 WAVELET TRANSFORM, SHORT-TIME FOURIER TRANSFORM AND HEISENBERG BOXES 442.13 ADAPTIVE TRANSFORMS: MATCHING PURSUITS 512.14 WAVELETS IN TWO OR MORE DIMENSIONS 552.15 THE CWT: COMPUTATION, BOUNDARY EFFECTS AND VIEWING 562.16 RIDGE FOLLOWING AND SECONDARY WAVELET FEATURE DECOUPLING 612.17 RIDGE HEIGHTS 662.18 RUNNING WAVELET ARCHETYPING 67
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