Multiresolution Signal Decomposition : Transforms, Subbands, and Wavelets

by Ali N. Akansu; Richard A. Haddad

• ISBN13: 9780120471409
• ISBN10: 012047140X
• Format: Hardcover
• Copyright: 1992-08-01
• Publisher: Academic Pr

Summary

This book provides an in-depth, integrated, and up-to-date exposition of the topic of signal decomposition techniques. Application areas of these techniques include speech and image processing, machine vision, information engineering, High-Definition Television, and telecommunications. The book will serve as the major reference for those entering the field, instructors teaching some or all of the topics in an advanced graduate course and researchers needing to consult an authoritative source. n The first book to give a unified and coherent exposition of multiresolutional signal decomposition techniques n Classroom tested textbook clearly describes the commonalities among three key methods-transform coding, and wavelet transforms n Gives comparative performance evaluations of many proposed techniques

Table of Contents

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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