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An Introduction to Wavelets : Volume 1 - Charles K. Chui

An Introduction to Wavelets

Volume 1

By: Charles K. Chui (Editor)

Hardcover

Published: 1st January 1992
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An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.
Key Features
* This is an introductory treatise on wavelet analysis, with an emphasis on spline-wavelets and time-frequency analysis
* This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis
* Suitable as a textbook for a beginning course on wavelet analysis

An Overview: From Fourier Analysis to Wavelet Analysis
The Integral Wavelet Transform and Time-Frequency Analysis
Inversion Formulas and Duals
Classification of Wavelets
Multiresolution Analysis, Splines, and Wavelets
Wavelet Decompositions and Reconstructions
Fourier Analysis: Fourier and Inverse Fourier Transforms
Continuous-Time Convolution and the Delta Function
Fourier Transform of Square-Integrable Functions
Fourier Series
Basic Convergence Theory and Poisson's Summation Formula
Wavelet Transforms and Time-Frequency Analysis: The Gabor Transform
Short-Time Fourier Transforms and the Uncertainty Principle
The Integral Wavelet Transform
Dyadic Wavelets and Inversions
Frames
Wavelet Series
Cardinal Spline Analysis: Cardinal Spline Spaces
B-Splines and Their Basic Properties
The Two-Scale Relation and an Interpolatory Graphical Display Algorithm
B-Net Representations and Computation of Cardinal Splines
Construction of Spline Approximation Formulas
Construction of Spline Interpolation Formulas
Scaling Functions and Wavelets: Multiresolution Analysis
Scaling Functions with Finite Two-Scale Relations
Direct-Sum Decompositions of L2(R)
Wavelets and Their Duals
Linear-Phase Filtering
Compactly Supported Wavelets
Cardinal Spline-Wavelets: Interpolaratory Spline-Wavelets
Compactly Supported Spline-Wavelets
Computation of Cardinal Spline-Wavelets
Euler-Frobenius Polynomials
Error Analysis in Spline-Wavelet Decomposition
Total Positivity, Complete Oscillation, Zero-Crossings
Orthogonal Wavelets and Wavelet Packets: Examples of Orthogonal Wavelets
Identification of Orthogonal Two-Scale Symbols
Construction of Compactly Supported Orthogonal Wavelets
Orthogonal Wavelet Packets
Orthogonal Decomposition of Wavelet Series
Notes
References
Subject Index
Appendix
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780121745844
ISBN-10: 0121745848
Series: Wavelet Analysis & Its Applications
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 266
Published: 1st January 1992
Publisher: ACADEMIC PR INC
Country of Publication: US
Dimensions (cm): 23.67 x 16.03  x 1.78
Weight (kg): 0.56