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Wavelets and Subbands : Fundamentals and Applications - A. Abbate

Wavelets and Subbands

Fundamentals and Applications

Hardcover

Published: 1st January 2002
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Recently there has been intense research activity on the subject of wavelet/subband theory and application. Experts in such diverse fields as mathematics, physics, electrical engineering and image processing have provided original and pioneering works and results. But this diversity, while rich and productive, has lead to a sense of fragmentation, especially to those new to the field, and nonspecialists, trying to understand the connections between the different aspects of wavelet and subband theory.

The book is designed to present an understanding of wavelets and their development from a continuous-domain transformation to a frame representation and finally to multiresolution analysis tools such as subband decomposition. The book presents a theoretical understanding of the subject that is intertwined with practical examples and practical applications of wavelets in ultrasonic and biomedical applications. There is special emphasis on applications in communications and compression as well as image processing.

Topics and Features:

* Provides an understanding of the link between continuous wavelet transform, the fast wavelet transform and subband decomposition.

* Algorithms and numerical examples are implemented in Matlab.

* The design of wavelet bases, and how to implement the transform both in hardware and software is discussed in detail.

* Covers the fundamentals and the developments of the links between areas such as time-frequency analysis, digital signal processing, image processing and Fourier and wavelet transform, both continuous and discrete.

Extended mathematical treatment and numerous examples, with particular emphasis to the transition from the continuous domain to multiresolution and subband. The book is an essential text/reference for graduates, researchers, and professionals in electrical engineering, communications engineering and computer engineering. Practitioners and professionals engaged in signal processing, wavelets and Fourier analysis will find the book a useful resource and comprehensive guide.

Prefacep. xiii
Notationp. xv
Introductionp. 1
Historical Review: From Fourier Analysis to Wavelet Analysis and Subbandp. 3
Organization of This Bookp. 8
Referencesp. 11
Fundamentalsp. 13
Wavelet Fundamentalsp. 15
Introductionp. 15
Why Wavelet Transforms?p. 18
Fourier Transform as a Wave Transformp. 20
Wavelet Transformp. 23
Connection Between Wavelets and Filtersp. 26
Time-Frequency Analysis: Short-Time Fourier Transform, Gabor Transform, and Tiling in the Time-Frequency Planep. 37
Examples of Waveletsp. 44
From the Continuous to the Discrete Casep. 47
Framesp. 49
Subbandsp. 53
Multiresolution Analysisp. 65
Matrix Formulationp. 69
Multiresolution Revisitedp. 72
Two-Dimensional Casep. 90
DWT and Subband Examplep. 92
Implementationsp. 95
Summary and Conclusionsp. 96
Referencesp. 97
Wavelets and Subbandsp. 101
Time and Frequency Analysis of Signalsp. 103
Introductionp. 103
Fundamentals of Signal Analysisp. 103
Uncertainty Principlep. 118
Windowed Fourier Transform: Short-Time Fourier Transform and Gabor Transformp. 121
General Properties of the Windowed Fourier Transformp. 131
Uncertainty Principle for Windowed Fourier Transformp. 136
Inverse Windowed Fourier Transformp. 146
Continuous Wavelet Transformp. 147
Mathematics of the Continuous Wavelet Transformp. 150
Properties of the Continuous Wavelet Transformp. 154
Inverse Wavelet Transformp. 160
Examples of Mother Waveletsp. 163
Analytic Wavelet Transformp. 166
Analytic Signalsp. 166
Analytic Wavelet Transform on Real Signalsp. 172
Physical Interpretation of an Analytic Signalp. 181
Quadratic Time-Frequency Distributionsp. 184
Referencesp. 186
Discrete Wavelet Transform: From Frames to Fast Wavelet Transformp. 189
Introductionp. 189
Fundamentals of Frame Theoryp. 193
Sampling Theoremp. 199
Wavelet Framesp. 202
Examples of Wavelet Framesp. 206
Time-Frequency Localizationp. 210
Orthonormal Discrete Wavelet Transformsp. 212
Multiresolution Analysisp. 218
Scaling Functionsp. 230
Construction of Wavelet Bases Using Multiresolution Analysisp. 237
Wavelet Basesp. 241
Shannon Waveletp. 244
Meyer Waveletp. 246
Haar Waveletp. 248
Battle-Lemarie (Spline) Waveletsp. 250
Daubechies Compactly Supported Waveletsp. 251
Fast Wavelet Transformp. 259
Biorthogonal Wavelet Basesp. 265
Referencesp. 270
Theory of Subband Decompositionp. 273
Introductionp. 273
Fundamentals of Digital Signal Processingp. 275
Multirate Systemsp. 278
Polyphase Decompositionp. 286
Two-Channel Filter Bank/PR Filterp. 298
Biorthogonal Filtersp. 307
Lifting Schemep. 310
M-Band Casep. 312
Applications of Multirate Filteringp. 322
Referencesp. 336
Two-Dimensional Wavelet Transforms and Applicationsp. 339
Introductionp. 339
Orthogonal Pyramid Transformsp. 341
Progressive Transforms for Lossless and Lossy Image Codingp. 348
Embedded Zerotree Waveletsp. 359
Referencesp. 379
Applicationsp. 383
Applications of Wavelets in the Analysis of Transient Signalsp. 385
Introductionp. 385
Introduction to Time-Frequency Analysis of Transient Signalsp. 387
Ultrasonic Systemsp. 388
Ultrasonic Characterization of Coatings by the Ridges of the Analytic Wavelet Transformp. 394
Characterization of Coatingsp. 404
Biomedical Application of Wavelets: Analysis of EEG Signals for Monitoring Depth of Anesthesiap. 407
Wavelet Spectral Analysis of EEG Signalsp. 412
System Response Wavelet Analysis of EEG Signalsp. 415
Discussion of Resultsp. 416
Referencesp. 417
Applications of Subband and Wavelet Transform in Communication Systemsp. 423
Introductionp. 423
Applications in Spread Spectrum Communication Systemsp. 425
Excisionp. 426
Adaptive Filter-Bank Exciserp. 433
Transform-Based Low Probability of Intercept Receiverp. 437
Application of Multirate Filter Bank in Spreading Code Generation and Multiple Accessp. 440
Modulation Using Filter Banks and Waveletsp. 446
Multitione Modulationp. 447
Noise Reduction in Audio and Images Using Waveletsp. 448
Audio/Video/Image Compressionp. 458
Progressive Pattern Recognitionp. 466
Referencesp. 469
Real-Time Implementations of Wavelet Transformsp. 473
Digital VLSI Implementationp. 473
Optical Implementationp. 481
Matrix Processing and Neural Networksp. 489
Acousto-Optic Devicesp. 490
Other Optical Implementationsp. 498
Referencesp. 503
Appendixp. 507
Fourier Transformp. 507
Discrete Fourier Transformp. 510
z-Transformp. 516
Orthogonal Representation of Signalsp. 517
Bibliographyp. 521
Indexp. 543
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780817641368
ISBN-10: 081764136X
Series: Applied and Numerical Harmonic Analysis
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 551
Published: 1st January 2002
Publisher: BIRKHAUSER BOSTON INC
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 3.18
Weight (kg): 1.01