Wavelets and subbands : fundamentals and applications : with 234 figures

Recently there has been intense research activity on the subjectof wavelet and subband theory. Experts in diverse fields such asmathematics, physics, electrical engineering, and image processinghave provided original and pioneering works and results. But thisdiversity, while rich and productive, has led to a sense offragmentation, especially to those new to the field and tononspecialists who are trying to understand the connections betweenthe different aspects of wavelet and subband theory.`Wavelets and Subbands' is designed to present an understandingof wavelets and their development from a continuous-domaintransformation to a frame representation and finally tomultiresolution analysis tools such as subband decomposition. The bookpresents a theoretical understanding of the subject that isintertwined with practical examples and applications of wavelets inultrasonic and biomedical domains. There is special emphasis onapplications in communications, compression, and image processing.Topics and Features: * Provides an understanding of the linkbetween the continuous wavelet transform, the fast wavelet transform,and subband decomposition * Algorithms and numerical examples areimplemented in MATLAB * Discusses the design of wavelet bases anddetails how to implement the transform both in hardware and software *Covers the fundamentals and the developments of the links betweenareas such as time-frequency analysis, digital signal processing,image processing, and Fourier and wavelet transform, both continuousand discrete * Offers extended mathematical treatment and numerousexamples, with particular emphasis on the transition from thecontinuous domain to multiresolution and subband decomposition.The book is an essential text and reference for graduates,researchers, and professionals in electrical engineering,

Preface	p. xiii
Notation	p. xv
1. Introduction	p. 1
1.1 Historical Review: From Fourier Analysis to Wavelet Analysis and Subband	p. 3
1.2 Organization of This Book	p. 8
1.3 References	p. 11
Part I Fundamentals	p. 13
2. Wavelet Fundamentals	p. 15
2.1 Introduction	p. 15
2.2 Why Wavelet Transforms?	p. 18
2.3 Fourier Transform as a Wave Transform	p. 20
2.4 Wavelet Transform	p. 23
2.5 Connection Between Wavelets and Filters	p. 26
2.6 Time-Frequency Analysis: Short-Time Fourier Transform, Gabor Transform, and Tiling in the Time-Frequency Plane	p. 37
2.7 Examples of Wavelets	p. 44
2.8 From the Continuous to the Discrete Case	p. 47
2.9 Frames	p. 49
2.10 Subbands	p. 53
2.11 Multiresolution Analysis	p. 65
2.12 Matrix Formulation	p. 69
2.13 Multiresolution Revisited	p. 72
2.14 Two-Dimensional Case	p. 90
2.15 DWT and Subband Example	p. 92
2.16 Implementations	p. 95
2.17 Summary and Conclusions	p. 96
2.18 References	p. 97
Part II Wavelets and Subbands	p. 101
3. Time and Frequency Analysis of Signals	p. 103
3.1 Introduction	p. 103
3.1.1 Fundamentals of Signal Analysis	p. 103
3.1.2 Uncertainty Principle	p. 118
3.2 Windowed Fourier Transform: Short-Time Fourier Transform and Gabor Transform	p. 121
3.2.1 General Properties of the Windowed Fourier Transform	p. 131
3.2.2 Uncertainty Principle for Windowed Fourier Transform	p. 136
3.2.3 Inverse Windowed Fourier Transform	p. 146
3.3 Continuous Wavelet Transform	p. 147
3.3.1 Mathematics of the Continuous Wavelet Transform	p. 150
3.3.2 Properties of the Continuous Wavelet Transform	p. 154
3.3.3 Inverse Wavelet Transform	p. 160
3.3.4 Examples of Mother Wavelets	p. 163
3.4 Analytic Wavelet Transform	p. 166
3.4.1 Analytic Signals	p. 166
3.4.2 Analytic Wavelet Transform on Real Signals	p. 172
3.4.3 Physical Interpretation of an Analytic Signal	p. 181
3.5 Quadratic Time-Frequency Distributions	p. 184
3.6 References	p. 186
4. Discrete Wavelet Transform: From Frames to Fast Wavelet Transform	p. 189
4.1 Introduction	p. 189
4.2 Fundamentals of Frame Theory	p. 193
4.3 Sampling Theorem	p. 199
4.4 Wavelet Frames	p. 202
4.5 Examples of Wavelet Frames	p. 206
4.6 Time-Frequency Localization	p. 210
4.7 Orthonormal Discrete Wavelet Transforms	p. 212
4.8 Multiresolution Analysis	p. 218
4.9 Scaling Functions	p. 230
4.10 Construction of Wavelet Bases Using Multiresolution Analysis	p. 237
4.11 Wavelet Bases	p. 241
4.11.1 Shannon Wavelet	p. 244
4.11.2 Meyer Wavelet	p. 246
4.11.3 Haar Wavelet	p. 248
4.11.4 Battle-Lemarie (Spline) Wavelets	p. 250
4.12 Daubechies Compactly Supported Wavelets	p. 251
4.13 Fast Wavelet Transform	p. 259
4.14 Biorthogonal Wavelet Bases	p. 265
4.15 References	p. 270
5. Theory of Subband Decomposition	p. 273
5.1 Introduction	p. 273
5.2 Fundamentals of Digital Signal Processing	p. 275
5.3 Multirate Systems	p. 278
5.4 Polyphase Decomposition	p. 286
5.5 Two-Channel Filter Bank/PR Filter	p. 298
5.6 Biorthogonal Filters	p. 307
5.7 Lifting Scheme	p. 310
5.8 M-Band Case	p. 312
5.9 Applications of Multirate Filtering	p. 322
5.10 References	p. 336
6. Two-Dimensional Wavelet Transforms and Applications	p. 339
6.1 Introduction	p. 339
6.2 Orthogonal Pyramid Transforms	p. 341
6.3 Progressive Transforms for Lossless and Lossy Image Coding	p. 348
6.4 Embedded Zerotree Wavelets	p. 359
6.5 References	p. 379
Part III Applications	p. 383
7. Applications of Wavelets in the Analysis of Transient Signals	p. 385
7.1 Introduction	p. 385
7.2 Introduction to Time-Frequency Analysis of Transient Signals	p. 387
7.2.1 Ultrasonic Systems	p. 388
7.2.2 Ultrasonic Characterization of Coatings by the Ridges of the Analytic Wavelet Transform	p. 394
7.2.3 Characterization of Coatings	p. 404
7.3 Biomedical Application of Wavelets: Analysis of EEG Signals for Monitoring Depth of Anesthesia	p. 407
7.3.1 Wavelet Spectral Analysis of EEG Signals	p. 412
7.3.2 System Response Wavelet Analysis of EEG Signals	p. 415
7.3.3 Discussion of Results	p. 416
7.4 References	p. 417
8. Applications of Subband and Wavelet Transform in Communication Systems	p. 423
8.1 Introduction	p. 423
8.2 Applications in Spread Spectrum Communication Systems	p. 425
8.2.1 Excision	p. 426
8.2.2 Adaptive Filter-Bank Exciser	p. 433
8.2.3 Transform-Based Low Probability of Intercept Receiver	p. 437
8.2.4 Application of Multirate Filter Bank in Spreading Code Generation and Multiple Access	p. 440
8.3 Modulation Using Filter Banks and Wavelets	p. 446
8.4 Multitione Modulation	p. 447
8.5 Noise Reduction in Audio and Images Using Wavelets	p. 448
8.6 Audio/Video/Image Compression	p. 458
8.6 Progressive Pattern Recognition	p. 466
8.7 References	p. 469
9. Real-Time Implementations of Wavelet Transforms	p. 473
9.1 Digital VLSI Implementation	p. 473
9.2 Optical Implementation	p. 481
9.2.1 Matrix Processing and Neural Networks	p. 489
9.2.2 Acousto-Optic Devices	p. 490
9.2.3 Other Optical Implementations	p. 498
9.3 References	p. 503
Appendix	p. 507
A. Fourier Transform	p. 507
B. Discrete Fourier Transform	p. 510
C. z-Transform	p. 516
D. Orthogonal Representation of Signals	p. 517
Bibliography	p. 521
Index	p. 543

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