Fundamentals of Wavelets Theory, Algorithms,

Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. This book provides a thorough treatment of wavelets from an engineering point of view. Updates to this edition include sections on lifting algorithms, edge detection, inverse problems, and Multiresolution Time Domain Method (MRTD). It is a one-stop source of theory, algorithms, applications, and computer codes related to wavelets for senior and graduate students in electrical engineering, physics and mathematics; research engineers and physicists; and design and software engineers in telecommunications and signal processing industries.

Jaideva C. Goswami, PhD, is an Engineering Advisor at Schlumberger in Sugarland, Texas. He is also a former professor of Electronics and Communication Engineering at the Indian Institute of Technology, Kharagpur. Dr. Goswami has taught several short courses on wavelets and contributed to the Wiley Encyclopedia of Electrical and Electronics Engineering as well as Wiley Encyclopedia of RF and Microwave Engineering. He has many research papers and patents to his credit, and is a Fellow of IEEE.

Andrew K. Chan, PhD, is on the faculty of Texas A&M University and is the coauthor of Wavelets in a Box and Wavelet Toolware. He is a Life Fellow of IEEE.

What is this book all about?
Mathematical Preliminary
Linear Spaces
Vectors and Vector Spaces
Basis Functions, Orthogonality and Biothogonality
Local Basis and Riesz Basis
Discrete Linear Normed Space
Approximation by Orthogonal Projection
Matrix Algebra and Linear Transformation
Digital Signals
Exercises
References
Fourier Analysis
Fourier Series
Rectified Sine Wave
Fourier Transform
Properties of Fourier Transform
Examples of Fourier Transform
Poisson's Sum and Partition of ZUnity
Sampling Theorem
Partial Sum and Gibb's Phenomenon
Fourier Analysis of Discrete-Time Signals
Discrete Fourier Transform (DFT)
Exercise
References
Time-Frequency Analysis
Window Function
Short-Time Fourier Transform
Discrete Short-Time Fourier Transform
Discrete Gabor Representation
Continuous Wavelet Transform
Discrete Wavelet Transform
Wavelet Series
Interpretations of the Time-Frequency Plot
Wigner-Ville Distribution
Properties of Wigner-Ville Distribution
Quadratic Superposition Principle
Ambiguity Function
Exercise
Computer Programs
References
Multiresolution Anaylsis
Multiresolution Spaces
Orthogonal, Biothogonal, and Semiorthogonal Decomposition
Two-Scale Relations
Decomposition Relation
Spline Functions and Properties
Mapping a Function into MRA Space
Exercise
Computer Programs
References
Construction of Wavelets
Necessary Ingredients for Wavelet Construction
Construction of Semiorthogonal Spline Wavelets
Construction of Orthonormal Wavelets
Orthonormal Scaling Functions
Construction of Biothogonal Wavelets
Graphical Display of Wavelet
Exercise
Computer Programs
References
DWT and Filter Bank Algorithms
Decimation and Interpolation
Signal Representation in the Approximation Subspace
Wavelet Decomposition Algorithm
Reconstruction Algorithm
Change of Bases
Signal Reconstruction in Semiorthogonal Subspaces
Examples
Two-Channel Perfect Reconstruction Filter Bank
Polyphase Representation for Filter Banks
Comments on DWT and PR Filter Banks
Exercise
Computer Program
References
Special Topics in Wavelets and Algorithms
Fast Integral Wavelet Transform
Ridgelet Transform
Curvelet Transform
Complex Wavelets
Lifting Wavelet transform
References
Digital Signal Processing Applications
Wavelet Packet
Wavelet-Packet Algorithms
Thresholding
Interference Suppression
Faulty Bearing Signature Identification
Two-Dimensional Wavelets and Wavelet Packets
Edge Detection
Image Compression
Microcalcification Cluster Detection
Table of Contents provided by Publisher. All Rights Reserved.

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Fundamentals of Wavelets Theory, Algorithms, and Applications

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