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