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9780120471409

Multiresolution Signal Decomposition : Transforms, Subbands, and Wavelets

by ;
  • ISBN13:

    9780120471409

  • ISBN10:

    012047140X

  • Format: Hardcover
  • Copyright: 1992-08-01
  • Publisher: Academic Pr

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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

Introductionp. 1
Introductionp. 1
Why Signal Decomposition?p. 2
Decompositions: Transforms, Subbands, and Waveletsp. 3
Block Transforms and Filter Banksp. 4
Multiresolution Structuresp. 7
The Synthesis/Analysis Structurep. 8
The Binomial-Hermite Sequences: A Unifying Examplep. 9
Performance Evaluation and Applicationsp. 9
Orthogonal Transformsp. 11
Signal Expansions in Orthogonal Functionsp. 12
Signal Expansionsp. 12
Least-Squares Interpretationp. 17
Block Transformsp. 19
The Two-Dimensional Transformationp. 24
Singular Value Decompositionp. 26
Transform Efficiency and Coding Performancep. 30
Decorrelation, Energy Compaction, and the KLTp. 30
Comparative Performance Measuresp. 37
Fixed Transformsp. 41
Sinusoidal Transformsp. 42
Discrete Polynomial Transformsp. 55
Rectangular Transformsp. 65
Block Transform Packetsp. 70
Parametric Modeling of Signal Sourcesp. 71
Autoregressive Signal Source Modelsp. 72
AR(1) Source Modelp. 73
Correlation Models for Imagesp. 74
Coefficient Variances in Orthogonal Transformsp. 76
Goodness of 2D Correlation Models for Imagesp. 80
Performance Comparison of Block Transformsp. 81
Lapped Orthogonal Transformsp. 86
Introductionp. 86
Properties of the LOTp. 88
An Optimized LOTp. 90
The Fast LOTp. 93
Energy Compaction Performance of the LOTsp. 95
2D Transform Implementationp. 97
Matrix Kronecker Product and Its Propertiesp. 97
Separability of 2D Transformsp. 99
Fast 2D Transformsp. 101
Transform Applicationsp. 102
Summaryp. 103
Theory of Subband Decompositionp. 113
Multirate Signal Processingp. 114
Decimation and Interpolationp. 114
Polyphase Decompositionp. 123
Bandpass and Modulated Signalsp. 128
Integer-Band Samplingp. 129
Quadrature Modulationp. 129
Mth Band, Mirror, and Power Complementary Filtersp. 134
Mth Band Filtersp. 134
Mirror Image Filtersp. 135
Power Complementary Filtersp. 137
Two-Channel Filter Banksp. 137
Two-Channel PR-QMF Bankp. 138
Regular Binary Subband Tree Structurep. 141
Irregular Binary Subband Tree Structurep. 146
Dyadic or Octave Band Subband Tree Structurep. 148
Laplacian Pyramid for Signal Decompositionp. 149
Modified Laplacian Pyramid for Critical Samplingp. 152
Generalized Subband Tree Structurep. 155
M-Band Filter Banksp. 156
The M-Band Filter Bank Structurep. 158
The Polyphase Decompositionp. 161
PR Requirements for FIR Filter Banksp. 170
The Paraunitary FIR Filter Bankp. 171
Time-Domain Representationsp. 180
Modulated Filter Banksp. 190
Cascaded Lattice Structuresp. 193
The Two-Band Lossless Latticep. 194
The M-Band Paraunitary Latticep. 197
The Two-Band Linear-Phase Latticep. 199
M-Band PR Linear Phase Filter Bankp. 203
Lattice Realizations of Modulated Filter Bankp. 206
IIR Subband Filter Banksp. 211
All-Pass Filters and Mirror Image Polynomialsp. 213
The Two-Band IIR QMF Structurep. 216
Perfect Reconstruction IIR Subband Systemsp. 218
Transmultiplexersp. 226
TDMA, FDMA, and CDMA Forms of the Transmultiplexerp. 227
Analysis of the Transmultiplexerp. 231
Orthogonal Transmultiplexerp. 235
Two-Dimensional Subband Decompositionp. 236
2D Transforms and Notationp. 236
Periodic Sequences and the DFTp. 237
Two-Dimensional Decimation and Interpolationp. 240
The 2D Filter Bankp. 245
Two-Band Filter Bank with Hexagonal or Quincunx Samplingp. 251
Fan Filter Banksp. 258
Summaryp. 259
Filter Bank Families: Design and Performancep. 271
Binomial QMF-Wavelet Filtersp. 271
Binomial QMF and Orthonormal Waveletsp. 276
Maximally Flat Filtersp. 278
Bernstein QMF-Wavelet Filtersp. 281
Johnston QMF Familyp. 286
Smith-Barnwell PR-CQF Familyp. 286
LeGall-Tabatabai PR Filter Bankp. 289
Princen-Bradley QMFp. 292
Optimal PR-QMF Design for Subband Image Codingp. 292
Parameters of Optimizationp. 293
Optimal PR-QMF Design: Energy Compactionp. 297
Optimal PR-QMF Design: Extended Set of Variablesp. 297
Samples of Optimal PR-QMFs and Performancep. 298
Performance of PR-QMF Familiesp. 304
Aliasing Energy in Multiresolution Decompositionp. 308
Aliasing Effects of Decimation/Interpolationp. 308
Nonaliasing Energy Ratiop. 313
G[subscript TC] and NER Performancep. 314
Quantization Effects in Filter Banksp. 315
Equivalent Noise Modelp. 316
Quantization Model for M-Band Codecp. 318
Optimal Design of Bit-Constrained, pdf-Optimized Filter Banksp. 323
Summaryp. 324
Time-Frequency Representationsp. 331
Introductionp. 331
Analog Background--Time Frequency Resolutionp. 332
The Short-Time Fourier Transformp. 341
The Continuous STFTp. 342
The Discrete STFTp. 343
The Discrete-Time STFT, or DFTp. 345
Discrete-Time Uncertainty and Binomial Sequencesp. 347
Discrete-Time Uncertaintyp. 347
Gaussian and Binomial Distributionsp. 350
Band-Pass Filtersp. 353
Time-Frequency Localizationp. 355
Localization in Traditional Block Transformsp. 355
Localization in Uniform M-Band Filter Banksp. 355
Localization in Dyadic and Irregular Treesp. 360
Block Transform Packetsp. 362
From Tiling Pattern to Block Transform Packetsp. 364
Signal Decomposition in Time-Frequency Planep. 373
From Signal to Optimum Tiling Patternp. 376
Signal Compactionp. 380
Interference Excisionp. 382
Summaryp. 384
Wavelet Transformp. 391
The Wavelet Transformp. 392
The Continuous Wavelet Transformp. 392
The Discrete Wavelet Transformp. 396
Multiresolution Signal Decompositionp. 401
Multiresolution Analysis Spacesp. 402
The Haar Waveletp. 404
Two-Band Unitary PR-QMF and Wavelet Basesp. 411
Multiresolution Pyramid Decompositionp. 416
Finite Resolution Wavelet Decompositionp. 421
The Shannon Waveletsp. 422
Initialization and the Fast Wavelet Transformp. 425
Wavelet Regularity and Wavelet Familiesp. 427
Regularity or Smoothnessp. 427
The Daubechies Waveletsp. 430
The Coiflet Basesp. 431
Biorthogonal Wavelets and Filter Banksp. 432
Discussions and Conclusionp. 437
Applicationsp. 443
Introductionp. 443
Analysis/Synthesis Configurationp. 444
Selection of Analysis and Synthesis Filtersp. 445
Spectral Effects of Down- and Up-samplersp. 446
Tree Structuring Algorithms for Hierarchical Subband Transformsp. 447
Subband Codingp. 448
Interference Excision in Direct Sequence Spread Spectrum Communicationsp. 452
Synthesis/Analysis Configurationp. 457
Discrete Multitone Modulation for Digital Communicationsp. 459
Spread Spectrum PR-QMF Codes for CDMA Communicationsp. 463
Resolution of the Identity and Inversionp. 473
Orthonormality in Frequencyp. 477
Problemsp. 479
Table of Contents provided by Syndetics. All Rights Reserved.

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