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

by Addison; Paul S

• ISBN13: 9780750306928
• ISBN10: 0750306920
• Format: Hardcover
• Copyright: 2002-07-15
• Publisher: CRC Press

Summary

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.

Author Biography

Paul Addison is a Reader in Fluid Mechanics at Napier University, Edinburgh. His research interests include fluid mechanics, non-destructive testing, medical signal analysis, wavelet transforms and fractal analysis. He is also a Director of CardioDigital Ltd, a company formed for the development and commercialization of pioneering work into the use of time-frequency decomposition techniques in medical signal analysis.

Table of Contents

Preface	xi
Getting started	1	(5)
Introduction	1	(1)
The wavelet transform	2	(1)
Reading the book	3	(3)
The continuous wavelet transform	6	(59)
Introduction	6	(1)
The wavelet	6	(3)
Requirements for the wavelet	9	(1)
The energy spectrum of the wavelet	9	(2)
The wavelet transform	11	(3)
Identification of coherent structures	14	(7)
Edge detection	21	(4)
The inverse wavelet transform	25	(3)
The signal energy: wavelet-based energy and power spectra	28	(5)
The wavelet transform in terms of the Fourier transform	33	(2)
Complex wavelets: the Morlet wavelet	35	(10)
The wavelet transform, short time Fourier transform and Heisenberg boxes	45	(6)
Adaptive transforms: matching pursuits	51	(4)
Wavelets in two or more dimensions	55	(1)
The CWT: computation, boundary effects and viewing	56	(7)
Endnotes	63	(2)
Chapter keywords and phrases	63	(1)
Further resources	63	(2)
The discrete wavelet transform	65	(79)
Introduction	65	(1)
Frames and orthogonal wavelet bases	65	(12)
Frames	65	(2)
Dyadic grid scaling and orthonormal wavelet transforms	67	(2)
The scaling function and the multiresolution representation	69	(3)
The scaling equation, scaling coefficients and associated wavelet equation	72	(1)
The Haar wavelet	73	(2)
Coefficients from coefficients: the fast wavelet transform	75	(2)
Discrete input signals of finite length	77	(14)
Approximations and details	77	(4)
The multiresolution algorithm--an example	81	(2)
Wavelet energy	83	(2)
Alternative indexing of dyadic grid coefficients	85	(2)
A simple worked example: the Haar wavelet transform	87	(4)
Everything discrete	91	(13)
Discrete experimental input signals	91	(5)
Smoothing, thresholding and denoising	96	(8)
Daubechies wavelets	104	(13)
Filtering	112	(3)
Symmlets and coiflets	115	(2)
Translation invariance	117	(2)
Biorthogonal wavelets	119	(2)
Two-dimensional wavelet transforms	121	(12)
Adaptive transforms: wavelet packets	133	(8)
Endnotes	141	(3)
Chapter keywords and phrases	141	(1)
Further resources	141	(3)
Fluids	144	(45)
Introduction	144	(1)
Statistical measures	145	(15)
Moments, energy and power spectra	145	(7)
Intermittency and correlation	152	(1)
Wavelet thresholding	153	(6)
Wavelet selection using entropy measures	159	(1)
Engineering flows	160	(18)
Jets, wakes, turbulence and coherent structures	160	(11)
Fluid-structure interaction	171	(3)
Two-dimensional flow fields	174	(4)
Geophysical flows	178	(9)
Atmospheric processes	178	(8)
Ocean processes	186	(1)
Other applications in fluids and further resources	187	(2)
Engineering testing, monitoring and characterization	189	(41)
Introduction	189	(1)
Machining processes: control, chatter, wear and breakage	189	(6)
Rotating machinery	195	(7)
Gears	195	(4)
Shafts, bearings and blades	199	(3)
Dynamics	202	(6)
Chaos	208	(3)
Non-destructive testing	211	(10)
Surface characterization	221	(3)
Other applications in engineering and further resources	224	(6)
Impacting	224	(1)
Data compression	225	(3)
Engines	228	(1)
Miscellaneous	229	(1)
Medicine	230	(48)
Introduction	230	(1)
The electrocardiogram	230	(18)
ECG timing, distortions and noise	231	(3)
Detection of abnormalities	234	(2)
Heart rate variability	236	(3)
Cardiac arrhythmias	239	(9)
ECG data compression	248	(1)
Neuroelectric waveforms	248	(10)
Evoked potentials and event-related potentials	249	(3)
Epileptic seizures and epileptogenic foci	252	(3)
Classification of the EEG using artificial neural networks	255	(3)
Pathological sounds, ultrasounds and vibrations	258	(9)
Blood flow sounds	259	(1)
Heart sounds and heart rates	260	(3)
Lung sounds	263	(1)
Acoustic response	264	(3)
Blood flow and blood pressure	267	(3)
Medical imaging	270	(5)
Ultrasonic images	270	(1)
Magnetic resonance imaging, computed tomography and other radiographic images	270	(3)
Optical imaging	273	(2)
Other applications in medicine	275	(3)
Electromyographic signals	275	(1)
Sleep apnoea	275	(1)
DNA	276	(1)
Miscellaneous	276	(1)
Further resources	277	(1)
Fractals, finance, geophysics and other areas	278	(36)
Introduction	278	(1)
Fractals	278	(16)
Exactly self-similar fractals	279	(3)
Stochastic fractals	282	(10)
Multifractals	292	(2)
Finance	294	(4)
Geophysics	298	(11)
Properties of subsurface media	299	(6)
Surface feature analysis	305	(2)
Climate, clouds, rainfall and river levels	307	(2)
Other areas	309	(5)
Astronomy	309	(1)
Chemistry and chemical engineering	310	(1)
Plasmas	311	(1)
Electrical systems	311	(1)
Sound and speech	312	(1)
Miscellaneous	313	(1)
Appendix Useful books, papers and websites	314	(3)
1 Useful books and papers	314	(1)
2 Useful websites	315	(2)
References	317	(34)
Index	351