An Introduction to Wavelets

, by Academic Press

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ISBN: 9780121745929 | 0121745929
Cover: Paperback

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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.

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An Introduction to Wavelets

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