The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance provides an overview of the theory and practical applications of wavelet transform methods. The author uses several hundred illustrations, some in color, to convey mathematical concepts and the results of applications. The first chapter presents a brief overview of the wavelet transform, including a short history. The remainder of the book is split into two parts: the first part discusses the mathematics of both discrete and continuous wavelet transforms while the second part deals with applications in a variety of subject areas, such as geophysics, medicine, fluid turbulence, engineering testing, speech and sound analysis, image analysis, and data compression. These application chapters make the reader aware of the similarities that exist in the use of wavelet transform analysis across disciplines. A comprehensive list of more than 700 references provides a valuable resource for further study. The book is designed specifically for the applied reader in science, engineering, medicine, finance, or any other of the growing number of application areas. Newcomers to the subject will find an accessible and clear account of the theory of continuous and discrete wavelet transforms, providing a large number of examples of their use across a wide range of disciplines. Readers already acquainted with wavelets can use the book to broaden their perspective.

Table of Contents:
PREFACE GETTING STARTED THE CONTINUOUS WAVELET TRANSFORM Introduction The Wavelet Requirements for the Wavelet The Energy Spectrum of the Wavelet The Wavelet Transform Identification of Coherent Structures Edge Detection The Inverse Wavelet Transform The Signal Energy: Wavelet-Based Energy and Power Spectra The Wavelet Transform in Terms of the Fourier Transform Complex Wavelets: The Morlet Wavelet The Wavelet Transform, Short Time Fourier Transform and Heisenberg Boxes Adaptive Transforms: Matching Pursuits Wavelets in Two or More Dimensions The CWT: Computation, Boundary Effects and Viewing Endnotes THE DISCRETE WAVELET TRANSFORM Introduction Frames and Orthogonal Wavelet Bases Discrete Input Signals of Finite Length Everything Discrete Daubechies Wavelets Translation Invariance Biorthogonal Wavelets Two-Dimensional Wavelet Transforms Adaptive Transforms: Wavelet Packets Endnotes FLUIDS Introduction Statistical Measures Engineering Flows Geophysical Flows Other Applications in Fluids and Further Resources ENGINEERING TESTING, MONITORING AND CHARACTERISATION Introduction Machining Processes: Control, Chatter, Wear and Breakage Rotating Machinery Dynamics Chaos Non-Destructive Testing Surface Characterisation Other Applications in Engineering and Further Resources MEDICINE Introduction The Electrocardiogram Neuroelectric Waveforms Pathological Sounds, Ultrasounds and Vibrations Blood Flow and Blood Pressure Medical Imaging Other Applications in Medicine FRACTALS, FINANCE, GEOPHYSICS AND OTHER AREAS Introduction Fractals Finance Geophysics Other Areas APPENDIX: USEFUL BOOKS, PAPERS AND WEBSITES Useful Books and Papers Useful Websites REFERENCES INDEX

Review :
"… nicely organized and thoroughly pedagogical handbook … The book is very much 'figure driven' and they are extremely useful for illustrating the mathematics and conveying the concepts in an uncomplicated matter … an eminently readable style in motivating and explaining wavelets throughout the course … this book, written as it is in a simple, forthright, and stimulating manner with balanced blend will prove a worthy addition to the understanding of wavelet transforms across disciplines." -Guruprasad Madhavan, Stony Brook Heart Center, IEEE-EMBS "The book works on two levels: it is an excellent introduction for readers new to wavelet transforms, and it is a useful source of information and some inspiration to anyone who has been working in the field for some time. … The book presents the field in an authoritative way but not too deeply. It has been designed as an overview and introduction to this dynamic area of computational analysis, and it achieves this with complete success. To conclude, I found this a thought provoking book on a fascinating subject: in fact once into the text I found it hard to put down." -Dr. K.O. Jones, Measurement+Control, Vol. 36/7, Sept. 2003 "The book is extremely well put together and lavishly illustrated (as one might infer from the title). … I largely enjoyed reading this book and I strongly recommend it to anyone with an interest in wavelets, or in the general field of signal processing for that matter." -Keith Worden, Journal of Sound and Vibration, 274 (2004) 1135-1136 "The book … provide[s] the reader with an overview of theory and practical applications of wavelet transforms methods, a new time-frequency decomposition tool for data analysis … The book can be recommended to the people interested above all in applications in science, engineering, medicine, finance, or elsewhere. An account of the theory of continuous and discrete wavelet transforms, with a large number of examples of their use across a wide range of disciplines, is convenient both for newcomers to the subject ad readers already acquainted with wavelets methods working in particular area of application." -Miloslav Duchori "Illustrations really do help in understanding wavelet transforms. It might be taken for granted that illustrations can aid in the understanding of a subject matter as this, but there is sound logical reasoning behind this claim that makes it especially true for this particular subject matter and also a great motivation for the text. This handbook goes the distance and shows that wavelet transforms are powerful data analysis tools that readily lend themselves to intuitive visual analysis and graphical representation, both of which can be critical to correct analysis in practice." -Raymond Martin