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Full Description
The Illustrated Wavelet Transform HandbookApplications 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.
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
