A first course in wavelets with Fourier analysis

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A first course in wavelets with Fourier analysis / Albert Boggess, Francis J. Narcowich

資料種別:

図書

出版情報:

Upper Saddle River, NJ : Prentice Hall, c2001

形態:

xix, 283 p. ; 25 cm

著者名:

ISBN:

9780130228093 [0130228095]

書誌ID:

BA52879309

子書誌情報

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書誌詳細

注記:

Includes bibliographical references (p. 279-280) and index
"Pearson Education"--Back cover

主題:

Fourier analysis; Wavelets (Mathematics)

言語:

英語

目次情報:

Preface

Acknowledgments

Inner Product Spaces / 0：

Motivation / 0.1：

Definition of Inner Product / 0.2：

The Spaces L[superscript 2] and l[superscript 2] / 0.3：

Definitions / 0.3.1：

Convergence in L[superscript 2] versus Uniform Convergence / 0.3.2：

Schwarz and Triangle Inequalities / 0.4：

Orthogonality / 0.5：

Definitions and Examples / 0.5.1：

Orthogonal Projections / 0.5.2：

Gram-Schmidt Orthogonalization / 0.5.3：

Linear Operators and Their Adjoints / 0.6：

Linear Operators / 0.6.1：

Adjoints / 0.6.2：

Least Squares and Linear Predictive Coding / 0.7：

Best Fit Line for Data / 0.7.1：

General Least Squares Algorithm / 0.7.2：

Linear Predictive Coding / 0.7.3：

Exercises / 0.8：

Fourier Series / 1：

Introduction / 1.1：

Historical Perspective / 1.1.1：

Signal Analysis / 1.1.2：

Partial Differential Equations / 1.1.3：

Computation of Fourier Series / 1.2：

On the Interval -[pi] [less than or equal] x [less than or equal] [pi] / 1.2.1：

Other Intervals / 1.2.2：

Cosine and Sine Expansions / 1.2.3：

Examples / 1.2.4：

The Complex Form of Fourier Series / 1.2.5：

Convergence Theorems for Fourier Series / 1.3：

The Riemann-Lebesgue Lemma / 1.3.1：

Convergence at a Point of Continuity / 1.3.2：

Convergence at a Point of Discontinuity / 1.3.3：

Uniform Convergence / 1.3.4：

Convergence in the Mean / 1.3.5：

The Fourier Transform / 1.4：

Informal Development of the Fourier Transform / 2.1：

The Fourier Inversion Theorem / 2.1.1：

Properties of the Fourier Transform / 2.1.2：

Basic Properties / 2.2.1：

Fourier Transform of a Convolution / 2.2.2：

Adjoint of the Fourier Transform / 2.2.3：

Plancherel Formula / 2.2.4：

Linear Filters / 2.3：

Time Invariant Filters / 2.3.1：

Causality and the Design of Filters / 2.3.2：

The Sampling Theorem / 2.4：

The Uncertainty Principle / 2.5：

Discrete Fourier Analysis / 2.6：

The Discrete Fourier Transform / 3.1：

Definition of Discrete Fourier Transform / 3.1.1：

Properties of the Discrete Fourier Transform / 3.1.2：

The Fast Fourier Transform / 3.1.3：

The FFT Approximation to the Fourier Transform / 3.1.4：

Application--Parameter Identification / 3.1.5：

Application--Discretizations of Ordinary Differential Equations / 3.1.6：

Discrete Signals / 3.2：

Time Invariant, Discrete Linear Filters / 3.2.1：

Z-Transform and Transfer Functions / 3.2.2：

Haar Wavelet Analysis / 3.3：

Why Wavelets? / 4.1：

Haar Wavelets / 4.2：

The Haar Scaling Function / 4.2.1：

Basic Properties of the Haar Scaling Function / 4.2.2：

The Haar Wavelet / 4.2.3：

Haar Decomposition and Reconstruction Algorithms / 4.3：

Decomposition / 4.3.1：

Reconstruction / 4.3.2：

Filters and Diagrams / 4.3.3：

Summary / 4.4：

Multiresolution Analysis / 4.5：

The Multiresolution Framework / 5.1：

Definition / 5.1.1：

The Scaling Relation / 5.1.2：

The Associated Wavelet and Wavelet Spaces / 5.1.3：

Decomposition and Reconstruction Formulas: A Tale of Two Bases / 5.1.4：

Implementing Decomposition and Reconstruction / 5.1.5：

The Decomposition Algorithm / 5.2.1：

The Reconstruction Algorithm / 5.2.2：

Processing a Signal / 5.2.3：

Fourier Transform Criteria / 5.3：

The Scaling Function / 5.3.1：

Orthogonality via the Fourier Transform / 5.3.2：

The Scaling Equation via the Fourier Transform / 5.3.3：

Iterative Procedure for Constructing the Scaling Function / 5.3.4：

The Daubechies Wavelets / 5.4：

Daubechies's Construction / 6.1：

Classification, Moments, and Smoothness / 6.2：

Computational Issues / 6.3：

The Scaling Function at Dyadic Points / 6.4：

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