This book is the only source available that presents a unified view of the theory and applications of discrete and continuous- time signals. This is the only book to present the mathematical point of view, as well as the discrete-time signal processing perspective. It brings together information previously available only in research papers, in engineering and applied mathematics. Appropriate for researchers and practitioners in signal processing and applied mathematics.
Author(s): C. S. Burrus, Ramesh A. Gopinath, Haitao Guo
Edition: 1
Publisher: Prentice Hall
Year: 1998
Language: English
Pages: 282
Tags: Физика;Матметоды и моделирование в физике;
Contents......Page 5
Preface......Page 11
1 Introduction to Wavelets......Page 15
1.1 Wavelets and Wavelet Expansion Systems......Page 16
1.2 The Discrete Wavelet Transform......Page 21
1.3 The Discrete-Time and Continuous Wavelet Transforms......Page 22
1.5 This Chapter......Page 23
2.1 Signal Spaces......Page 24
2.2 The Scaling Function......Page 25
2.3 The Wavelet Functions......Page 28
2.4 The Discrete Wavelet Transform......Page 31
2.6 Display of the Discrete Wavelet Transform and the Wavelet Expansion......Page 32
2. 7 Examples of Wavelet Expansions......Page 34
2.8 An Example of the Haar Wavelet System......Page 37
3.1 Analysis - From Fine Scale to Coarse Scale......Page 45
3.2 Synthesis - From Coarse Scale to Fine Scale......Page 50
3.3 Input Coefficients......Page 51
3.5 Different Points of View......Page 52
4.1 Bases, Orthogonal Bases, and Biorthogonal Bases......Page 55
4.2 Frames and Tight Frames......Page 59
4.3 Conditional and Unconditional Bases......Page 62
5.1 Tools and Definitions......Page 64
5.2 Necessary Conditions......Page 67
5.3 Freque"!cy Domain Necessary Conditions......Page 68
5.4 Sufficient Conditions......Page 70
5.5 The Wavelet......Page 72
5. 7 Example Scaling Functions and Wavelets......Page 73
5.8 Further Properties of the Scaling Function and Wavelet......Page 76
5.9 Parameterization of the Scaling Coefficients......Page 79
5.10 Calculating the Basic Scaling Function and Wavelet......Page 81
6.1 K-Regular Scaling Filters......Page 87
6.2 Vanishing Wavelet Moments......Page 89
6.3 Daubechies' Method for Zero Wavelet Moment Design......Page 90
6.5 Relation of Zero Wavelet Moments to Smoothness......Page 97
6. 7 Approximation of Signals by Scaling Function Projection......Page 100
6.8 Approximation of Scaling Coefficients by Samples of the Signal......Page 101
6.9 Coiflets and Related Wavelet Systems......Page 102
6.10 Minimization of Moments Rather than Zero Moments......Page 111
7.1 Tiling the Time-Frequency or Time-Scale Plane......Page 112
7.2 Multiplicity-M (M-Band) Scaling Functions and Wavelets......Page 116
7.3 Wavelet Packets......Page 124
7.4 Biorthogonal Wavelet Systems......Page 128
7.5 Multiwavelets......Page 136
7.6 Overcomplete Representations, Frames, Redundant Transforms, and Adaptive Bases......Page 142
7. 7 Local Trigonometric Bases......Page 148
7.8 Discrete Multi resolution Analysis, the Discrete-Time Wavelet Transform, and the Continuous Wavelet Transform......Page 155
8.1 Introduction......Page 162
8.2 Unitary Filter Banks......Page 169
8.3 Unitary Filter Banks-Some Illustrative Examples......Page 174
8.4 M-band Wavelet Tight Frames......Page 176
8.5 Modulated Filter Banks......Page 178
8.6 Modulated Wavelet Tight Frames......Page 182
8.7 Linear Phase Filter Banks......Page 183
8.8 Linear-Phase Wavelet Tight Frames......Page 190
8.9 Linear-Phase Modulated Filter Banks......Page 191
8.10 Linear Phase Modulated Wavelet Tight Frames......Page 192
8.11 Time-Varying Filter Bank Trees......Page 193
8.12 Filter Banks and Wavelets-Summary......Page 200
9.1 Finite Wavelet Expansions and Transforms......Page 202
9.2 Periodic or Cyclic Discrete Wavelet Transform......Page 204
9.3 Filter Bank Structures for Calculation of the DWT and Complexity......Page 205
9.4 The Periodic Case......Page 206
9.5 Structure of the Periodic Discrete Wavelet Transform......Page 208
9.6 More General Structures......Page 209
10.1 Wavelet-Based Signal Processing......Page 210
10.2 Approximate FFT using the Discrete Wavelet Transform......Page 211
10.3 Nonlinear Filtering or Denoising with the DWT......Page 219
10.4 Statistical Estimation......Page 225
10.5 Signal and Image Compression......Page 226
10.6 Why are Wavelets so Useful?......Page 230
10.7 Applications......Page 231
10.8 Wavelet Software......Page 232
11.1 Properties of the Basic Multiresolution Scaling Function......Page 233
11.2 Types of Wavelet Systems......Page 235
12 References......Page 237
Bibliography......Page 238
Appendix A. Derivations for Chapter 5 on Scaling Functions......Page 260
Appendix B. Derivations for Section on Properties......Page 267
Appendix C. Matlab Programs......Page 272
Index......Page 280
