Multiresolution Signal Decomposition - Transforms, Subbands, and Wavelets

Contents......Page 8
1.1 Introduction......Page 18
1.2 Why Signal Decomposition?......Page 19
1.3 Decompositions: Transforms, Subbands, and Wavelets......Page 20
1.4 Performance Evaluation and Applications......Page 26
2 Orthogonal Transforms......Page 28
2.1 Signal Expansions in Orthogonal Functions......Page 29
2.2 Transform Efficiency and Coding Performance......Page 47
2.3 Fixed Transforms......Page 58
2.4 Parametric Modeling of Signal Sources......Page 88
2.5 Lapped Orthogonal Transforms......Page 103
2.6 2D Transform Implementation......Page 114
2.7 Summary......Page 120
3 Theory of Subband Decomposition......Page 130
3.1 Multirate Signal Processing......Page 131
3.2 Bandpass and Modulated Signals......Page 145
5.2 Analog Background—Time Frequency Resolution......Page 0
3.4 Two-Channel Filter Banks......Page 154
3.5 M-Band Filter Banks......Page 173
3.6 Cascaded Lattice Structures......Page 210
3.7 IIR Subband Filter Banks......Page 228
3.8 Transmultiplexers......Page 243
3.9 Two-Dimensional Subband Decomposition......Page 253
3.10 Summary......Page 276
4.1 Binomial QMF-Wavelet Filters......Page 288
4.2 Maximally Flat Filters......Page 295
4.3 Bernstein QMF-Wavelet Filters......Page 298
4.5 Smith-Barnwell PR-CQF Family......Page 303
4.6 LeGall-Tabatabai PR Filter Bank......Page 306
4.8 Optimal PR-QMF Design for Subband Image Coding......Page 309
4.9 Performance of PR-QMF Families......Page 321
4.10 Aliasing Energy in Multiresolution Decomposition......Page 325
4.11 G[sub(TC)] and NER Performance......Page 331
4.12 Quantization Effects in Filter Banks......Page 332
4.13 Summary......Page 341
5.1 Introduction......Page 348
5.3 The Short-Time Fourier Transform......Page 358
5.4 Discrete-Time Uncertainty and Binomial Sequences......Page 364
5.5 Time-Frequency Localization......Page 372
5.6 Block Transform Packets......Page 379
6 Wavelet Transform......Page 408
6.1 The Wavelet Transform......Page 409
6.2 Multiresolution Signal Decomposition......Page 418
6.3 Wavelet Regularity and Wavelet Families......Page 444
6.4 Biorthogonal Wavelets and Filter Banks......Page 449
6.5 Discussions and Conclusion......Page 454
7.1 Introduction......Page 460
7.2 Analysis/Synthesis Configuration......Page 461
7.3 Synthesis/Analysis Configuration......Page 474
A: Resolution of the Identity and Inversion......Page 490
B: Orthonormality in Frequency......Page 494
C: Problems......Page 496
Index......Page 514