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

Transcription

1 The Illustrated Wavelet Transform Handbook Introductory Theory and Applications in Science, Engineering, Medicine and Finance Paul S Addison Napier University, Edinburgh, UK IoP Institute of Physics Publishing Bristol and Philadelphia

2 Preface xi 1 Getting started T 1.1 Introduction The wavelet transform Reading the book 3 2 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 Chapter keywords and phrases Further resources 63 3 The discrete wavelet transform Introduction Frames and orthogonal wavelet bases Frames 65 vi l

3 Vlll Dyadic grid scaling and orthonormal wavelet transforms The scaling function and the multiresolution representation The scaling equation, scaling coefficients and associated wavelet equation The Haar wavelet Coefficients from coefficients: the fast wavelet transform Discrete input signals of finite length Approximations and details The multiresolution algorithm an example Wavelet energy Alternative indexing of dyadic grid coefficients A simple worked example: the Haar wavelet transform Everything discrete Discrete experimental input signals Smoothing, thresholding and denoising Daubechies wavelets Filtering Symmlets and coiflets Translation invariance Biorthogonal wavelets Two-dimensional wavelet transforms Adaptive transforms: wavelet packets Endnotes Chapter keywords and phrases Further resources Fluids Introduction Statistical measures Moments, energy and power spectra Intermittency and correlation Wavelet thresholding Wavelet selection using entropy measures Engineering flows Jets, wakes, turbulence and coherent structures Fluid-structure interaction Two-dimensional flow fields Geophysical flows Atmospheric processes Ocean processes Other applications in fluids and further resources Engineering testing, monitoring and characterization Introduction Machining processes: control, chatter, wear and breakage Rotating machinery 195

4 Gears Shafts, bearings and blades Dynamics Chaos Non-destructive testing Surface characterization Other applications in engineering and further resources Impacting Data compression Engines Miscellaneous ix Me( licine Introduction The electrocardiogram ECG timing, distortions and noise Detection of abnormalities Heart rate variability Cardiac arrhythmias ECG data compression Neuroelectric waveforms Evoked potentials and event-related potentials Epileptic seizures and epileptogenic foci Classification of the EEG using artificial neural networks Pathological sounds, ultrasounds and vibrations Blood flow sounds Heart sounds and heart rates Lung sounds Acoustic response Blood flow and blood pressure Medical imaging Ultrasonic images Magnetic resonance imaging, computed tomography and other radiographic images Optical imaging Other applications in medicine Electromyographic signals Sleep apnoea DNA Miscellaneous Further resources Fractals, finance, geophysics and other areas 7.1 Introduction 7.2 Fractals Exactly self-similar fractals

5 X Stochastic fractals Multifractals Finance Geophysics Properties of subsurface media Surface feature analysis Climate, clouds, rainfall and river levels Other areas Astronomy Chemistry and chemical engineering Plasmas Electrical systems Sound and speech Miscellaneous 313 Appendix Useful books, papers and websites Useful books and papers Useful websites 315 References 317 Index 351