| Preface | p. xiii |
| Notation | p. xv |
| Introduction | p. 1 |
| Historical Review: From Fourier Analysis to Wavelet Analysis and Subband | p. 3 |
| Organization of This Book | p. 8 |
| References | p. 11 |
| Fundamentals | p. 13 |
| Wavelet Fundamentals | p. 15 |
| Introduction | p. 15 |
| Why Wavelet Transforms? | p. 18 |
| Fourier Transform as a Wave Transform | p. 20 |
| Wavelet Transform | p. 23 |
| Connection Between Wavelets and Filters | p. 26 |
| Time-Frequency Analysis: Short-Time Fourier Transform, Gabor Transform, and Tiling in the Time-Frequency Plane | p. 37 |
| Examples of Wavelets | p. 44 |
| From the Continuous to the Discrete Case | p. 47 |
| Frames | p. 49 |
| Subbands | p. 53 |
| Multiresolution Analysis | p. 65 |
| Matrix Formulation | p. 69 |
| Multiresolution Revisited | p. 72 |
| Two-Dimensional Case | p. 90 |
| DWT and Subband Example | p. 92 |
| Implementations | p. 95 |
| Summary and Conclusions | p. 96 |
| References | p. 97 |
| Wavelets and Subbands | p. 101 |
| Time and Frequency Analysis of Signals | p. 103 |
| Introduction | p. 103 |
| Fundamentals of Signal Analysis | p. 103 |
| Uncertainty Principle | p. 118 |
| Windowed Fourier Transform: Short-Time Fourier Transform and Gabor Transform | p. 121 |
| General Properties of the Windowed Fourier Transform | p. 131 |
| Uncertainty Principle for Windowed Fourier Transform | p. 136 |
| Inverse Windowed Fourier Transform | p. 146 |
| Continuous Wavelet Transform | p. 147 |
| Mathematics of the Continuous Wavelet Transform | p. 150 |
| Properties of the Continuous Wavelet Transform | p. 154 |
| Inverse Wavelet Transform | p. 160 |
| Examples of Mother Wavelets | p. 163 |
| Analytic Wavelet Transform | p. 166 |
| Analytic Signals | p. 166 |
| Analytic Wavelet Transform on Real Signals | p. 172 |
| Physical Interpretation of an Analytic Signal | p. 181 |
| Quadratic Time-Frequency Distributions | p. 184 |
| References | p. 186 |
| Discrete Wavelet Transform: From Frames to Fast Wavelet Transform | p. 189 |
| Introduction | p. 189 |
| Fundamentals of Frame Theory | p. 193 |
| Sampling Theorem | p. 199 |
| Wavelet Frames | p. 202 |
| Examples of Wavelet Frames | p. 206 |
| Time-Frequency Localization | p. 210 |
| Orthonormal Discrete Wavelet Transforms | p. 212 |
| Multiresolution Analysis | p. 218 |
| Scaling Functions | p. 230 |
| Construction of Wavelet Bases Using Multiresolution Analysis | p. 237 |
| Wavelet Bases | p. 241 |
| Shannon Wavelet | p. 244 |
| Meyer Wavelet | p. 246 |
| Haar Wavelet | p. 248 |
| Battle-Lemarie (Spline) Wavelets | p. 250 |
| Daubechies Compactly Supported Wavelets | p. 251 |
| Fast Wavelet Transform | p. 259 |
| Biorthogonal Wavelet Bases | p. 265 |
| References | p. 270 |
| Theory of Subband Decomposition | p. 273 |
| Introduction | p. 273 |
| Fundamentals of Digital Signal Processing | p. 275 |
| Multirate Systems | p. 278 |
| Polyphase Decomposition | p. 286 |
| Two-Channel Filter Bank/PR Filter | p. 298 |
| Biorthogonal Filters | p. 307 |
| Lifting Scheme | p. 310 |
| M-Band Case | p. 312 |
| Applications of Multirate Filtering | p. 322 |
| References | p. 336 |
| Two-Dimensional Wavelet Transforms and Applications | p. 339 |
| Introduction | p. 339 |
| Orthogonal Pyramid Transforms | p. 341 |
| Progressive Transforms for Lossless and Lossy Image Coding | p. 348 |
| Embedded Zerotree Wavelets | p. 359 |
| References | p. 379 |
| Applications | p. 383 |
| Applications of Wavelets in the Analysis of Transient Signals | p. 385 |
| Introduction | p. 385 |
| Introduction to Time-Frequency Analysis of Transient Signals | p. 387 |
| Ultrasonic Systems | p. 388 |
| Ultrasonic Characterization of Coatings by the Ridges of the Analytic Wavelet Transform | p. 394 |
| Characterization of Coatings | p. 404 |
| Biomedical Application of Wavelets: Analysis of EEG Signals for Monitoring Depth of Anesthesia | p. 407 |
| Wavelet Spectral Analysis of EEG Signals | p. 412 |
| System Response Wavelet Analysis of EEG Signals | p. 415 |
| Discussion of Results | p. 416 |
| References | p. 417 |
| Applications of Subband and Wavelet Transform in Communication Systems | p. 423 |
| Introduction | p. 423 |
| Applications in Spread Spectrum Communication Systems | p. 425 |
| Excision | p. 426 |
| Adaptive Filter-Bank Exciser | p. 433 |
| Transform-Based Low Probability of Intercept Receiver | p. 437 |
| Application of Multirate Filter Bank in Spreading Code Generation and Multiple Access | p. 440 |
| Modulation Using Filter Banks and Wavelets | p. 446 |
| Multitione Modulation | p. 447 |
| Noise Reduction in Audio and Images Using Wavelets | p. 448 |
| Audio/Video/Image Compression | p. 458 |
| Progressive Pattern Recognition | p. 466 |
| References | p. 469 |
| Real-Time Implementations of Wavelet Transforms | p. 473 |
| Digital VLSI Implementation | p. 473 |
| Optical Implementation | p. 481 |
| Matrix Processing and Neural Networks | p. 489 |
| Acousto-Optic Devices | p. 490 |
| Other Optical Implementations | p. 498 |
| References | p. 503 |
| Appendix | p. 507 |
| Fourier Transform | p. 507 |
| Discrete Fourier Transform | p. 510 |
| z-Transform | p. 516 |
| Orthogonal Representation of Signals | p. 517 |
| Bibliography | p. 521 |
| Index | p. 543 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
