Fundamentals of Wavelets Theory, Algorithms, and Applications Se....pdf

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Cover Page

WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING

Title Page

ISBN 9780470484135

Contents

Preface to the Second Edition xv

Preface to the First Edition xvii

1 What Is This Book All About? 1

2 Mathematical Preliminary 6

3 Fourier Analysis 34

4 Time-Frequency Analysis 61

5 Multiresolution Analysis 94

6 Construction of Wavelets 114

7 DWT and Filter Bank Algorithms 147

8 Special Topics in Wavelets and Algorithms 197

9 Digital Signal Processing Applications 239

10 Wavelets in Boundary Value Problems 308

Index 353

Preface to the Second Edition

Preface to the First Edition

1 What Is This Book All About?

2 Mathematical Preliminary

2.1 LINEAR SPACES

2.2 VECTORS AND VECTOR SPACES

2.3 BASIS FUNCTIONS, ORTHOGONALITY, AND BIORTHOGONALITY

2.3.1 Example

2.3.2 Orthogonality and Biorthogonality

2.4 LOCAL BASIS AND RIESZ BASIS

2.4.1 Haar Basis

2.4.2 Shannon Basis

2.5 DISCRETE LINEAR NORMED SPACE

2.5.1 Example 1

2.5.2 Example 2

2.6 APPROXIMATION BY ORTHOGONAL PROJECTION

2.7 MATRIX ALGEBRA AND LINEAR TRANSFORMATION

2.7.1 Elements of Matrix Algebra

2.7.2 Eigenmatrix

2.7.3 Linear Transformation

2.7.4 Change of Basis

2.7.5 Hermitian Matrix, Unitary Matrix, and Orthogonal Transformation

2.8 DIGITAL SIGNALS

2.8.1 Sampling of Signal

2.8.2 Linear Shift Invariant Systems

2.8.3 Convolution

2.8.4 z - Transform

2.8.5 Region of Convergence

2.8.6 Inverse z - Transform

2.9 EXERCISES

2.10 REFERENCES

3 Fourier Analysis

3.1 FOURIER SERIES

3.2 EXAMPLES

3.2.1 Rectified Sine Wave

3.2.2 Comb Function and the Fourier Series Kernel KN(t)

3.3 FOURIER TRANSFORM

3.4 PROPERTIES OF FOURIER TRANSFORM

3.4.1 Linearity

3.4.2 Time Shifting and Time Scaling

3.4.3 Frequency Shifting and Frequency Scaling

3.4.4 Moments

3.4.5 Convolution

3.4.6 Parseval's Theorem

3.5 EXAMPLES OF FOURIER TRANSFORM

3.5.1 The Rectangular Pulse

3.5.2 The Triangular Pulse

3.5.3 The Gaussian Function

3.6 POISSON'S SUM AND PARTITION OF UNITY

3.6.1 Partition of Unity

3.7 SAMPLING THEOREM

3.8 PARTIAL SUM AND GIBB'S PHENOMENON

3.9 FOURIER ANALYSIS OF DISCRETE TIME SIGNALS

3.9.1 Discrete Fourier Basis and Discrete Fourier Series

3.9.2 Discrete Time Fourier Transform ( DTFT )

3.10 DISCRETE FOURIER TRANSFORM ( DFT )

3.11 EXERCISES

3.12 REFERENCES

4 Time Frequency Analysis

4.1 WINDOW FUNCTION

4.2 SHORT TIME FOURIER TRANSFORM

4.2.1 Inversion Formula

4.2.2 Gabor Transform

4.2.3 Time Frequency Window

4.2.4 Properties of STFT

4.3 DISCRETE SHORT TIME FOURIER TRANSFORM

4.4 DISCRETE GABOR REPRESENTATION

4.5 CONTINUOUS WAVELET TRANSFORM

4.5.1 Inverse Wavelet Transform

4.5.2 Time Frequency Window

4.6 DISCRETE WAVELET TRANSFORM

4.7 WAVELET SERIES

4.8 INTERPRETATIONS OF THE TIME FREQUENCY PLOT

4.9 WIGNER VILLE DISTRIBUTION

4.9.1 Gaussian Modulated Chirp

4.9.2 Sinusoidal Modulated Chirp

4.9.3 Sinusoidal Signal

4.10 PROPERTIES OF WIGNER VILLE DISTRIBUTION

4.10.1 A Real Quantity

4.10.2 Marginal Properties

4.10.3 Correlation Function

4.11 QUADRATIC SUPERPOSITION PRINCIPLE

4.12 AMBIGUITY FUNCTION

4.13 EXERCISES

4.14 COMPUTER PROGRAMS

4.14.1 Short Time Fourier Transform

4.14.2 Wigner Ville Distribution

4.15 REFERENCES

5 Multiresolution Analysis

5.1 MULTIRESOLUTION SPACES

5.2 ORTHOGONAL, BIORTHOGONAL, AND SEMIORTHOGONAL DECOMPOSITION

5.3 TWO SCALE RELATIONS

5.4 DECOMPOSITION RELATION

5.5 SPLINE FUNCTIONS AND PROPERTIES

5.5.1 Properties of Splines

5.6 MAPPING A FUNCTION INTO MRA SPACE

5.6.1 Linear Splines (m=2)

5.6.2 Cubic Splines (m=4)

5.7 EXERCISES

5.8 COMPUTER PROGRAMS 5.8.1 B Splines

5.9 REFERENCES

6 Construction of Wavelets

6.1 NECESSARY INGREDIENTS FOR WAVELET CONSTRUCTION

6.1.1 Relationship between the Two Scale Sequences

6.1.2 Relationship between Reconstruction and Decomposition Sequences

6.2 CONSTRUCTION OF SEMIORTHOGONAL SPLINE WAVELETS

6.2.1 Expression for {g0[k]}

6.2.2 Remarks

6.3 CONSTRUCTION OF ORTHONORMAL WAVELETS

6.4 ORTHONORMAL SCALING FUNCTIONS

6.4.1 Shannon Scaling Function

6.4.2 Meyer Scaling Function

6.4.3 Battle Lemarié Scaling Function

6.4.4 Daubechies Scaling Function

6.5 CONSTRUCTION OF BIORTHOGONAL WAVELETS

6.6 GRAPHICAL DISPLAY OF WAVELET

6.6.1 Iteration Method

6.6.2 Spectral Method

6.6.3 Eigenvalue Method

6.7 EXERCISES

6.8 COMPUTER PROGRAMS

6.8.1 Daubechies Wavelet

6.8.2 Iteration Method

6.9 REFERENCES

7 DWT and Filter Bank Algorithms

7.1 DECIMATION AND INTERPOLATION

7.1.1 Decimation

7.1.2 Interpolation

7.1.3 Convolution Followed by Decimation

7.1.4 Interpolation Followed by Convolution

7.2 SIGNAL REPRESENTATION IN THE APPROXIMATION SUBSPACE

7.3 WAVELET DECOMPOSITION ALGORITHM

7.4 RECONSTRUCTION ALGORITHM

7.5 CHANGE OF BASES

7.6 SIGNAL RECONSTRUCTION IN SEMIORTHOGONAL SUBSPACES

7.6.1 Change of Basis for Spline Functions

7.6.2 Change of Basis for Spline Wavelets

7.7 EXAMPLES

7.8 TWO CHANNEL PERFECT RECONSTRUCTION FILTER BANK

7.8.1 Spectral Domain Analysis of a Two Channel PR Filter Bank

7.8.2 Time Domain Analysis

7.9 POLYPHASE REPRESENTATION FOR FILTER BANKS

7.9.1 Signal Representation in Polyphase Domain

7.9.2 Filter Bank in the Polyphase Domain

7.10 COMMENTS ON DWT AND PR FILTER BANKS

7.11 EXERCISES

7.12 COMPUTER PROGRAM

7.12.1 Decomposition and Reconstruction Algorithm

7.13 REFERENCES

8 Special Topics in Wavelets and Algorithms

8.1 FAST INTEGRAL WAVELET TRANSFORM

8.1.1 Finer Time Resolution

8.1.2 Finer Scale Resolution

8.1.3 Function Mapping into the Interoctave Approximation Subspaces

8.1.4 Examples

8.2 RIDGELET TRANSFORM

8.3 CURVELET TRANSFORM

8.4 COMPLEX WAVELETS

8.4.1 Linear Phase Biorthogonal Approach

8.4.2 Quarter Shift Approach

8.4.3 Common Factor Approach

8.5 LIFTING WAVELET TRANSFORM

8.5.1 Linear Spline Wavelet

8.5.2 Construction of Scaling Function and Wavelet from Lifting Scheme

8.5.3 Linear Interpolative Subdivision

8.6 REFERENCES

9 Digital Signal Processing Applications

9.1 WAVELET PACKET

9.2 WAVELET PACKET ALGORITHMS

9.3 THRESHOLDING

9.3.1 Hard Thresholding

9.3.2 Soft Thresholding

9.3.3 Percentage Thresholding

9.3.4 Implementation

9.4 INTERFERENCE SUPPRESSION

9.4.1 Best Basis Selection

9.5 FAULTY BEARING SIGNATURE IDENTIFICATION

9.5.1 Pattern Recognition of Acoustic Signals

9.5.2 Wavelets, Wavelet Packets, and FFT Features

9.6 TWO DIMENSIONAL WAVELETS AND WAVELET PACKETS

9.6.1 Two Dimensional Wavelets

9.6.2 Two Dimensional Wavelet Packets

9.6.3 Two Dimensional Wavelet Algorithm

9.6.4 Wavelet Packet Algorithm

9.7 EDGE DETECTION

9.7.1 Sobel Edge Detector

9.7.2 Laplacian of Gaussian Edge Detector

9.7.3 Canny Edge Detector

9.7.4 Wavelet Edge Detector

9.8 IMAGE COMPRESSION

9.8.1 Basics of Data Compression

9.8.2 Wavelet Tree Coder

9.8.3 EZW Code

9.8.4 EZW Example

9.8.5 Spatial Oriented Tree ( SOT )

9.8.6 Generalized Self Similarity Tree ( GST )

9.9 MICROCALCIFICATION CLUSTER DETECTION

9.9.1 CAD Algorithm Structure

9.9.2 Partitioning of Image and Nonlinear Contrast Enhancement

9.9.3 Wavelet Decomposition of the Subimages

9.9.4 Wavelet Coefficient Domain Processing

9.9.5 Histogram Thresholding and Dark Pixel Removal

9.9.6 Parametric ART 2 Clustering

9.9.7 Results

9.10 MULTICARRIER COMMUNICATION SYSTEMS ( MCCS )

9.10.1 OFDM Multicarrier Communication Systems

9.10.2 Wavelet Packet – Based MCCS

9.11 THREE DIMENSIONAL MEDICAL IMAGE VISUALIZATION

9.11.1 Three Dimensional Wavelets and Algorithms

9.11.2 Rendering Techniques

9.11.3 Region of Interest

9.11.4 Summary

9.12 GEOPHYSICAL APPLICATIONS

9.12.1 Boundary Value Problems and Inversion

9.12.2 Well Log Analysis

9.12.3 Reservoir Data Analysis

9.12.4 Downhole Pressure Gauge Data Analysis

9.13 COMPUTER PROGRAMS

9.13.1 Two Dimensional Wavelet Algorithms

9.13.2 Wavelet Packet Algorithms

9.14 REFERENCES

10 Wavelets in Boundary Value Problems

10.1 INTEGRAL EQUATIONS

10.2 METHOD OF MOMENTS

10.3 WAVELET TECHNIQUES

10.3.1 Use of Fast Wavelet Algorithm

10.3.2 Direct Application of Wavelets

10.3.3 Wavelets in Spectral Domain

10.3.4 Wavelet Packets

10.4 WAVELETS ON THE BOUNDED INTERVAL

10.5 SPARSITY AND ERROR CONSIDERATIONS

10.6 NUMERICAL EXAMPLES

10.7 SEMIORTHOGONAL VERSUS ORTHOGONAL WAVELETS

10.8 DIFFERENTIAL EQUATIONS

10.8.1 Multigrid Method

10.8.2 Multiresolution Time Domain ( MRTD ) Method

10.8.3 Haar MRTD Derivation

10.8.4 Subcell Modeling in MRTD

10.8.5 Examples

10.9 EXPRESSIONS FOR SPLINES AND WAVELETS

10.10 REFERENCES

Index

Back Page

WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING KAI CHANG, Editor Texas A & M University FIBER - OPTIC COMMUNICATION SYSTEMS, Fourth Edition Govind P. Agrawal ASYMMETRIC PASSIVE COMPONENTS IN MICROWAVE INTEGRATED CIRCUITS Hee - Ran Ahn COHERENT OPTICAL COMMUNICATIONS SYSTEMS Silvello Betti, Giancarlo De Marchis, and Eugenio Iannone PHASED ARRAY ANTENNAS: FLOQUET ANALYSIS, SYNTHESIS, BFNs, AND AC TIVE ARRAY SYSTEMS Arun K. Bhattacharyya HIGH - FREQUENCY ELECTROMAGNETIC TECHNIQUES: RECENT ADVANCES AND APPLICATIONS Asoke K. Bhattacharyya RADIO PROPAGATION AND ADAPTIVE ANTENNAS FOR WIRELESS COMMUNICATION LINKS: TERRESTRIAL, ATMOSPHERIC, AND IONOSPHERIC Nathan Blaunstein and Christos G. Christodoulou COMPUTATIONAL METHODS FOR ELECTROMAGNETICS AND MICROWAVES Richard C. Booton, Jr. ELECTROMAGNETIC SHIELDING Salvatore Celozzi, Rodolfo Araneo, and Giampiero Lovat MICROWAVE RING CIRCUITS AND ANTENNAS Kai Chang MICROWAVE SOLID - STATE CIRCUITS AND APPLICATIONS Kai Chang RF AND MICROWAVE WIRELESS SYSTEMS Kai Chang RF AND MICROWAVE CIRCUIT AND COMPONENT DESIGN FOR WIRELESS SYSTEMS Kai Chang, Inder Bahl, and Vijay Nair MICROWAVE RING CIRCUITS AND RELATED STRUCTURES, Second Edition Kai Chang and Lung - Hwa Hsieh MULTIRESOLUTION TIME DOMAIN SCHEME FOR ELECTROMAGNETIC ENGINEERING Yinchao Chen, Qunsheng Cao, and Raj Mittra DIODE LASERS AND PHOTONIC INTEGRATED CIRCUITS Larry Coldren and Scott Corzine EM DETECTION OF CONCEALED TARGETS David J. Daniels RADIO FREQUENCY CIRCUIT DESIGN W. Alan Davis and Krishna Agarwal RADIO FREQUENCY CIRCUIT DESIGN, Second Edition W. Alan Davis MULTICONDUCTOR TRANSMISSION - LINE STRUCTURES: MODAL ANALYSIS TECHNIQUES J. A. Brand ã o Faria PHASED ARRAY - BASED SYSTEMS AND APPLICATIONS Nick Fourikis SOLAR CELLS AND THEIR APPLICATIONS, Second Edition Lewis M. Fraas and Larry D. Partain FUNDAMENTALS OF MICROWAVE TRANSMISSION LINES Jon C. Freeman OPTICAL SEMICONDUCTOR DEVICES Mitsuo Fukuda MICROSTRIP CIRCUITS Fred Gardiol both.indd 361 both.indd 361 11/9/2010 10:11:09 AM 11/9/2010 10:11:09 AM

HIGH - SPEED VLSI INTERCONNEC TIONS, Second Edition Ashok K. Goel FUNDAMENTALS OF WAVELETS: THEORY, ALGORITHMS, AND APPLICATIONS, Second Edition Jaideva C. Goswami and Andrew K. Chan HIGH - FREQUENCY ANALOG INTEGRATED CIRCUIT DESIGN Ravender Goyal (ed.) ANALYSIS AND DESIGN OF INTEGRATED CIRCUIT ANTENNA MODULES K. C. Gupta and Peter S. Hall PHASED ARRAY ANTENNAS, Second Edition R. C. Hansen STRIPLINE CIRCULATORS Joseph Helszajn THE STRIPLINE CIRCULATOR: THEORY AND PRACTICE Joseph Helszajn LOCALIZED WAVES Hugo E. Hern á ndez - Figueroa, Michel Zamboni - Rached, and Erasmo Recami (eds.) MICROSTRIP FILTERS FOR RF/MICROWAVE APPLICATIONS Jia - Sheng Hong and M. J. Lancaster MICROWAVE APPROACH TO HIGHLY IRREGULAR FIBER OPTICS Huang Hung - Chia NONLINEAR OPTICAL COMMUNICATION NETWORKS Eugenio Iannone, Francesco Matera, Antonio Mecozzi, and Marina Settembre FINITE ELEMENT SOFTWARE FOR MICROWAVE ENGINEERING Tatsuo Itoh, Giuseppe Pelosi, and Peter P. Silvester (eds.) INFRARED TECHNOLOGY: APPLICATIONS TO ELECTROOPTICS, PHOTONIC DEVICES, AND SENSORS A. R. Jha SUPERCONDUCTOR TECHNOLOGY: APPLICATIONS TO MICROWAVE, ELEC TRO - OPTICS, ELECTRICAL MACHINES, AND PROPULSION SYSTEMS A. R. Jha TIME AND FREQUENCY DOMAIN SOLUTIONS OF EM PROBLEMS USING INTEGTRAL EQUATIONS AND A HYBRID METHODOLOGY B. H. Jung, T. K. Sarkar, S. W. Ting, Y. Zhang, Z. Mei, Z. Ji, M. Yuan, A. De, M. Salazar - Palma, and S. M. Rao OPTICAL COMPUTING: AN INTRODUCTION M. A. Karim and A. S. S. Awwal INTRODUCTION TO ELEC TROMAGNETIC AND MICROWAVE ENGINEERING Paul R. Karmel, Gabriel D. Colef, and Raymond L. Camisa MILLIMETER WAVE OPTICAL DIELECTRIC INTEGRATED GUIDES AND CIRCUITS Shiban K. Koul ADVANCED INTEGRATED COMMUNICATION MICROSYSTEMS Joy Laskar, Sudipto Chakraborty, Manos Tentzeris, Franklin Bien, and Anh - Vu Pham MICROWAVE DEVICES, CIRCUITS AND THEIR INTERACTION Charles A. Lee and G. Conrad Dalman ADVANCES IN MICROSTRIP AND PRINTED ANTENNAS Kai - Fong Lee and Wei Chen (eds.) SPHEROIDAL WAVE FUNCTIONS IN ELEC TROMAGNETIC THEORY Le - Wei Li, Xiao - Kang Kang, and Mook - Seng Leong ARITHMETIC AND LOGIC IN COMPUTER SYSTEMS Mi Lu OPTICAL FILTER DESIGN AND ANALYSIS: A SIGNAL PROCESSING APPROACH Christi K. Madsen and Jian H. Zhao THEORY AND PRACTICE OF INFRARED TECHNOLOGY FOR NONDESTRUCTIVE TESTING Xavier P. V. Maldague METAMATERIALS WITH NEGATIVE PARAMETERS: THEORY, DESIGN, AND MICROWAVE APPLICATIONS Ricardo Marqu é s, Ferran Mart í n, and Mario Sorolla OPTOELECTRONIC PACKAGING A. R. Mickelson, N. R. Basavanhally, and Y. C. Lee (eds.) both.indd 362 both.indd 362 11/9/2010 10:11:09 AM 11/9/2010 10:11:09 AM

OPTICAL CHARACTER RECOGNITION Shunji Mori, Hirobumi Nishida, and Hiromit su Yamada ANTENNAS FOR RADAR AND COMMUNICATIONS: A POLARIMETRIC APPROACH Harold Mott INTEGRATED ACTIVE ANTENNAS AND SPATIAL POWER COMBINING Julio A. Navarro and Kai Chang ANALYSIS METHODS FOR RF, MICROWAVE, AND MILLIMETER - WAVE PLANAR TRANSMISSION LINE STRUCTURES Cam Nguyen LASER DIODES AND THEIR APPLICATIONS TO COMMUNICATIONS AND INFORMATION PROCESSING Takahiro Numai FREQUENCY CONTROL OF SEMICONDUCTOR LASERS Motoichi Oht su (ed.) WAVELETS IN ELEC TROMAGNETICS AND DEVICE MODELING George W. Pan OPTICAL SWITCHING Georgios Papadimitriou, Chrisoula Papazoglou, and Andreas S. Pomportsis MICROWAVE IMAGING Matteo Pastorino ANALYSIS OF MULTICONDUCTOR TRANSMISSION LINES Clayton R. Paul INTRODUCTION TO ELECTROMAGNETIC COMPATIBILITY, Second Edition Clayton R. Paul ADAPTIVE OPTICS FOR VISION SCIENCE: PRINCIPLES, PRACTICES, DESIGN AND APPLICATIONS Jason Porter, Hope Queener, Julianna Lin, Karen Thorn, and Abdul Awwal (eds.) ELECTROMAGNETIC OPTIMIZATION BY GENETIC ALGORITHMS Yahya Rahmat - Samii and Eric Michielssen (eds.) INTRODUCTION TO HIGH - SPEED ELEC TRONICS AND OPTOELECTRONICS Leonard M. Riaziat NEW FRONTIERS IN MEDICAL DEVICE TECHNOLOGY Arye Rosen and Harel Rosen (eds.) ELECTROMAGNETIC PROPAGATION IN MULTI - MODE RANDOM MEDIA Harrison E. Rowe ELECTROMAGNETIC PROPAGATION IN ONE - DIMENSIONAL RANDOM MEDIA Harrison E. Rowe HISTORY OF WIRELESS Tapan K. Sarkar, Robert J. Mailloux, Arthur A. Oliner, Magdalena Salazar - Palma, and Dipak L. Sengupta PHYSICS OF MULTIANTENNA SYSTEMS AND BROADBAND PROCESSING Tapan K. Sarkar, Magdalena Salazar - Palma, and Eric L. Mokole SMART ANTENNAS Tapan K. Sarkar, Michael C. Wicks, Magdalena Salazar - Palma, and Robert J. Bonneau NONLINEAR OPTICS E. G. Sauter APPLIED ELECTROMAGNETICS AND ELECTROMAGNETIC COMPATIBILITY Dipak L. Sengupta and Valdis V. Liepa COPLANAR WAVEGUIDE CIRCUITS, COMPONENTS, AND SYSTEMS Rainee N. Simons ELECTROMAGNETIC FIELDS IN UNCONVENTIONAL MATERIALS AND STRUCTURES Onkar N. Singh and Akhlesh Lakhtakia (eds.) ANALYSIS AND DESIGN OF AUTONOMOUS MICROWAVE CIRCUITS Almudena Su á rez ELECTRON BEAMS AND MICROWAVE VACUUM ELECTRONICS Shulim E. Tsimring FUNDAMENTALS OF GLOBAL POSITIONING SYSTEM RECEIVERS: A SOFTWARE APPROACH, Second Edition James Bao - yen Tsui both.indd 363 both.indd 363 11/9/2010 10:11:09 AM 11/9/2010 10:11:09 AM

RF/MICROWAVE INTERACTION WITH BIOLOGICAL TISSUES Andr é Vander Vorst, Arye Rosen, and Youji Kotsuka InP - BASED MATERIALS AND DEVICES: PHYSICS AND TECHNOLOGY Osamu Wada and Hideki Hasegawa (eds.) COMPACT AND BROADBAND MICROSTRIP ANTENNAS Kin - Lu Wong DESIGN OF NONPLANAR MICROSTRIP ANTENNAS AND TRANSMISSION LINES Kin - Lu Wong PLANAR ANTENNAS FOR WIRELESS COMMUNICATIONS Kin - Lu Wong FREQUENCY SELECTIVE SURFACE AND GRID ARRAY T. K. Wu (ed.) ACTIVE AND QUASI - OPTICAL ARRAYS FOR SOLID - STATE POWER COMBINING Robert A. York and Zoya B. Popovi c´ (eds.) OPTICAL SIGNAL PROCESSING, COMPUTING AND NEURAL NETWORKS Francis T. S. Yu and Suganda Jutamulia ELECTROMAGNETIC SIMULATION TECHNIQUES BASED ON THE FDTD METHOD Wenhua Yu, Xiaoling Yang, Yongjun Liu, and Raj Mittra SiGe, GaAs, AND InP HETEROJUNCTION BIPOLAR TRANSISTORS Jiann Yuan PARALLEL SOLUTION OF INTEGRAL EQUATION - BASED EM PROBLEMS Yu Zhang and Tapan K. Sarkar ELECTRODYNAMICS OF SOLIDS AND MICROWAVE SUPERCONDUCTIVITY Shu - Ang Zhou both.indd 364 both.indd 364 11/9/2010 10:11:09 AM 11/9/2010 10:11:09 AM

Fundamentals of Wavelets ffirs01.indd i ffirs01.indd i 11/9/2010 10:18:54 AM 11/9/2010 10:18:54 AM

WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING KAI CHANG, Editor Texas A&M University A complete list of the titles in this series appears at the end of this volume. ffirs02.indd ii ffirs02.indd ii 11/9/2010 10:18:55 AM 11/9/2010 10:18:55 AM

Fundamentals of Wavelets Theory, Algorithms, and Applications Second Edition JAIDEVA C. GOSWAMI ANDREW K. CHAN JOHN WILEY & SONS, INC., PUBLICATION ffirs03.indd iii ffirs03.indd iii 11/9/2010 10:18:55 AM 11/9/2010 10:18:55 AM

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