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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 |
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