The illustrated wavelet transform handbook : introductory theory and applications in science, engineering, medicine and finance / Paul S. Addison.

Format:

Book

Author/Creator:

Addison, Paul S.

Contributor:

John G. Hartman Memorial Library Fund.

Language:

English

Subjects (All):

Wavelets (Mathematics).

Physical Description:

xiii, 353 pages : illustrations (some color) ; 25 cm

Place of Publication:

Bristol : Institute of Physics Publishing, [2002]

Summary:

This book 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 book first presents an overview of the wavelet transform, followed by a discussion of the mathematics of both discrete and continuous wavelet transforms. The book concludes with applications in a variety of subject areas, making 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.

Contents:

1.2 The wavelet transform 2

2 The continuous wavelet transform 6

2.2 The wavelet 6

2.3 Requirements for the wavelet 9

2.4 The energy spectrum of the wavelet 9

2.5 The wavelet transform 11

2.6 Identification of coherent structures 14

2.7 Edge detection 21

2.8 The inverse wavelet transform 25

2.9 The signal energy: wavelet-based energy and power spectra 28

2.10 The wavelet transform in terms of the Fourier transform 33

2.11 Complex wavelets: the Morlet wavelet 35

2.12 The wavelet transform, short time Fourier transform and Heisenberg boxes 45

2.13 Adaptive transforms: matching pursuits 51

2.14 Wavelets in two or more dimensions 55

2.15 The CWT: computation, boundary effects and viewing 56

2.16.1 Chapter keywords and phrases 63

3 The discrete wavelet transform 65

3.2 Frames and orthogonal wavelet bases 65

3.2.1 Frames 65

3.2.2 Dyadic grid scaling and orthonormal wavelet transforms 67

3.2.3 The scaling function and the multiresolution representation 69

3.2.4 The scaling equation, scaling coefficients and associated wavelet equation 72

3.2.5 The Haar wavelet 73

3.2.6 Coefficients from coefficients: the fast wavelet transform 75

3.3 Discrete input signals of finite length 77

3.3.1 Approximations and details 77

3.3.2 The multiresolution algorithm

an example 81

3.3.3 Wavelet energy 83

3.3.4 Alternative indexing of dyadic grid coefficients 85

3.3.5 A simple worked example: the Haar wavelet transform 87

3.4 Everything discrete 91

3.4.1 Discrete experimental input signals 91

3.4.2 Smoothing, thresholding and denoising 96

3.5 Daubechies wavelets 104

3.5.1 Filtering 112

3.5.2 Symmlets and coiflets 115

3.6 Translation invariance 117

3.7 Biorthogonal wavelets 119

3.8 Two-dimensional wavelet transforms 121

3.9 Adaptive transforms: wavelet packets 133

3.10.1 Chapter keywords and phrases 141

4 Fluids 144

4.2 Statistical measures 145

4.2.1 Moments, energy and power spectra 145

4.2.2 Intermittency and correlation 152

4.2.3 Wavelet thresholding 153

4.2.4 Wavelet selection using entropy measures 159

4.3 Engineering flows 160

4.3.1 Jets, wakes, turbulence and coherent structures 160

4.3.2 Fluid-structure interaction 171

4.3.3 Two-dimensional flow fields 174

4.4 Geophysical flows 178

4.4.1 Atmospheric processes 178

4.4.2 Ocean processes 186

4.5 Other applications in fluids and further resources 187

5 Engineering testing, monitoring and characterization 189

5.2 Machining processes: control, chatter, wear and breakage 189

5.3 Rotating machinery 195

5.3.1 Gears 195

5.3.2 Shafts, bearings and blades 199

5.4 Dynamics 202

5.5 Chaos 208

5.6 Non-destructive testing 211

5.7 Surface characterization 221

5.8 Other applications in engineering and further resources 224

5.8.1 Impacting 224

5.8.2 Data compression 225

5.8.3 Engines 228

6 Medicine 230

6.2 The electrocardiogram 230

6.2.1 ECG timing, distortions and noise 231

6.2.2 Detection of abnormalities 234

6.2.3 Heart rate variability 236

6.2.4 Cardiac arrhythmias 239

6.2.5 ECG data compression 248

6.3 Neuroelectric waveforms 248

6.3.1 Evoked potentials and event-related potentials 249

6.3.2 Epileptic seizures and epileptogenic foci 252

6.3.3 Classification of the EEG using artificial neural networks 255

6.4 Pathological sounds, ultrasounds and vibrations 258

6.4.1 Blood flow sounds 259

6.4.2 Heart sounds and heart rates 260

6.4.3 Lung sounds 263

6.4.4 Acoustic response 264

6.5 Blood flow and blood pressure 267

6.6 Medical imaging 270

6.6.1 Ultrasonic images 270

6.6.2 Magnetic resonance imaging, computed tomography and other radiographic images 270

6.6.3 Optical imaging 273

6.7 Other applications in medicine 275

6.7.1 Electromyographic signals 275

6.7.2 Sleep apnoea 275

6.7.3 DNA 276

7 Fractals, finance, geophysics and other areas 278

7.2 Fractals 278

7.2.1 Exactly self-similar fractals 279

7.2.2 Stochastic fractals 282

7.2.3 Multifractals 292

7.3 Finance 294

7.4 Geophysics 298

7.4.1 Properties of subsurface media 299

7.4.2 Surface feature analysis 305

7.4.3 Climate, clouds, rainfall and river levels 307

7.5 Other areas 309

7.5.1 Astronomy 309

7.5.2 Chemistry and chemical engineering 310

7.5.3 Plasmas 311

7.5.4 Electrical systems 311

7.5.5 Sound and speech 312.

Notes:

Includes bibliographic references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the John G. Hartman Memorial Library Fund.

ISBN:

0750306920

OCLC:

47939469