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Tables of Contents for Multiresolution Signal Decomposition
Chapter/Section Title
Page #
Page Count
Introduction
1
10
Introduction
1
1
Why Signal Decomposition?
2
1
Decompositions: Transforms, Subbands, and Wavelets
3
6
Block Transforms and Filter Banks
4
3
Multiresolution Structures
7
1
The Synthesis/Analysis Structure
8
1
The Binomial-Hermite Sequences: A Unifying Example
9
1
Performance Evaluation and Applications
9
2
Orthogonal Transforms
11
102
Signal Expansions in Orthogonal Functions
12
18
Signal Expansions
12
5
Least-Squares Interpretation
17
2
Block Transforms
19
5
The Two-Dimensional Transformation
24
2
Singular Value Decomposition
26
4
Transform Efficiency and Coding Performance
30
11
Decorrelation, Energy Compaction, and the KLT
30
7
Comparative Performance Measures
37
4
Fixed Transforms
41
30
Sinusoidal Transforms
42
13
Discrete Polynomial Transforms
55
10
Rectangular Transforms
65
5
Block Transform Packets
70
1
Parametric Modeling of Signal Sources
71
15
Autoregressive Signal Source Models
72
1
AR(1) Source Model
73
1
Correlation Models for Images
74
2
Coefficient Variances in Orthogonal Transforms
76
4
Goodness of 2D Correlation Models for Images
80
1
Performance Comparison of Block Transforms
81
5
Lapped Orthogonal Transforms
86
11
Introduction
86
2
Properties of the LOT
88
2
An Optimized LOT
90
3
The Fast LOT
93
2
Energy Compaction Performance of the LOTs
95
2
2D Transform Implementation
97
6
Matrix Kronecker Product and Its Properties
97
2
Separability of 2D Transforms
99
2
Fast 2D Transforms
101
1
Transform Applications
102
1
Summary
103
10
Theory of Subband Decomposition
113
158
Multirate Signal Processing
114
14
Decimation and Interpolation
114
9
Polyphase Decomposition
123
5
Bandpass and Modulated Signals
128
6
Integer-Band Sampling
129
1
Quadrature Modulation
129
5
Mth Band, Mirror, & Power Complementary Filters
134
3
Mth Band Filters
134
1
Mirror Image Filters
135
2
Power Complementary Filters
137
1
Two-Channel Filter Banks
137
19
Two-Channel PR-QMF Bank
138
3
Regular Binary Subband Tree Structure
141
5
Irregular Binary Subband Tree Structure
146
2
Dyadic or Octave Band Subband Tree Structure
148
1
Laplacian Pyramid for Signal Decomposition
149
3
Modified Laplacian Pyramid for Critical Sampling
152
3
Generalized Subband Tree Structure
155
1
M-Band Filter Banks
156
37
The M-Band Filter Bank Structure
158
3
The Polyphase Decomposition
161
9
PR Requirements for FIR Filter Banks
170
1
The Paraunitary FIR Filter Bank
171
9
Time-Domain Representations
180
10
Modulated Filter Banks
190
3
Cascaded Lattice Structures
193
18
The Two-Band Lossless Lattice
194
3
The M-Band Paraunitary Lattice
197
2
The Two-Band Linear-Phase Lattice
199
4
M-Band PR Linear Phase Filter Bank
203
3
Lattice Realizations of Modulated Filter Bank
206
5
IIR Subband Filter Banks
211
15
All-Pass Filters and Mirror Image Polynomials
213
3
The Two-Band IIR QMF Structure
216
2
Perfect Reconstruction IIR Subband Systems
218
8
Transmultiplexers
226
10
TDMA, FDMA, and CDMA Forms of the Transmultiplexer
227
4
Analysis of the Transmultiplexer
231
4
Orthogonal Transmultiplexer
235
1
Two-Dimensional Subband Decomposition
236
23
2D Transforms and Notation
236
1
Periodic Sequences and the DFT
237
3
Two-Dimensional Decimation and Interpolation
240
5
The 2D Filter Bank
245
6
Two-Band Filter Bank with Hexagonal or Quincunx Sampling
251
7
Fan Filter Banks
258
1
Summary
259
12
Filter Bank Families: Design and Performance
271
60
Binomial QMF-Wavelet Filters
271
7
Binomial QMF and Orthonormal Wavelets
276
2
Maximally Flat Filters
278
3
Bernstein QMF-Wavelet Filters
281
5
Johnston QMF Family
286
1
Smith-Barnwell PR-CQF Family
286
3
LeGall-Tabatabai PR Filter Bank
289
3
Princen-Bradley QMF
292
1
Optimal PR-QMF Design for Subband Image Coding
292
12
Parameters of Optimization
293
4
Optimal PR-QMF Design: Energy Compaction
297
1
Optimal PR-QMF Design: Extended Set of Variables
297
1
Samples of Optimal PR-QMFs and Performance
298
6
Performance of PR-QMF Families
304
4
Aliasing Energy in Multiresolution Decomposition
308
6
Aliasing Effects of Decimation/Interpolation
308
5
Nonaliasing Energy Ratio
313
1
GTC and NER Performance
314
1
Quantization Effects in Filter Banks
315
9
Equivalent Noise Model
316
2
Quantization Model for M-Band Codec
318
5
Optimal Design of Bit-Constrained, pdf-Optimized Filter Banks
323
1
Summary
324
7
Time-Frequency Representations
331
60
Introduction
331
1
Analog Background---Time Frequency Resolution
332
9
The Short-Time Fourier Transform
341
6
The Continuous STFT
342
1
The Discrete STFT
343
2
The Discrete-Time STFT, or DFT
345
2
Discrete-Time Uncertainty and Binomial Sequences
347
8
Discrete-Time Uncertainty
347
3
Gaussian and Binomial Distributions
350
3
Band-Pass Filters
353
2
Time-Frequency Localization
355
7
Localization in Traditional Block Transforms
355
1
Localization in Uniform M-Band Filter Banks
355
5
Localization in Dyadic and Irregular Trees
360
2
Block Transform Packets
362
29
From Tiling Pattern to Block Transform Packets
364
9
Signal Decomposition in Time-Frequency Plane
373
3
From Signal to Optimum Tiling Pattern
376
4
Signal Compaction
380
2
Interference Excision
382
2
Summary
384
7
Wavelet Transform
391
52
The Wavelet Transform
392
9
The Continuous Wavelet Transform
392
4
The Discrete Wavelet Transform
396
5
Multiresolution Signal Decomposition
401
26
Multiresolution Analysis Spaces
402
2
The Haar Wavelet
404
7
Two-Band Unitary PR-QMF and Wavelet Bases
411
5
Multiresolution Pyramid Decomposition
416
5
Finite Resolution Wavelet Decomposition
421
1
The Shannon Wavelets
422
3
Initialization and the Fast Wavelet Transform
425
2
Wavelet Regularity and Wavelet Families
427
5
Regularity or Smoothness
427
3
The Daubechies Wavelets
430
1
The Coiflet Bases
431
1
Biorthogonal Wavelets and Filter Banks
432
5
Discussions and Conclusion
437
6
Applications
443
30
Introduction
443
1
Analysis/Synthesis Configuration
444
13
Selection of Analysis and Synthesis Filters
445
1
Spectral Effects of Down- and Up-samplers
446
1
Tree Structuring Algorithms for Hierarchical Subband Transforms
447
1
Subband Coding
448
4
Interference Excision in Direct Sequence Spread Spectrum Communications
452
5
Synthesis/Analysis Configuration
457
16
Discrete Multitone Modulation for Digital Communications
459
4
Spread Spectrum PR-QMF Codes for CDMA Communications
463
10
A Resolution of the Identity and Inversion
473
4
B Orthonormality in Frequency
477
2
C Problems
479