Wavelets : A Mathematical Tool for Signal Analysis (Mathematical Modeling and Computation)

Chui, Charles K.

Society for Industrial & Applied Mathematics,U.S.（1997/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 228 p.
• 言語 ENG
• 商品コード 9780898713848
• DDC分類 515.2433

Full Description

Wavelets continue to be powerful mathematical tools that can be used to solve problems for which the Fourier (spectral) method does not perform well or cannot handle. This book is for engineers, applied mathematicians, and other scientists who want to learn about using wavelets to analyze, process, and synthesize images and signals. Applications are described in detail and there are step-by-step instructions about how to construct and apply wavelets. The only mathematically rigorous monograph written by a mathematician specifically for nonspecialists, it describes the basic concepts of these mathematical techniques, outlines the procedures for using them, compares the performance of various approaches, and provides information for problem solving, putting the reader at the forefront of current research.

New methods and important topics described in the book include the following:

Multidimensional and multifrequency wavelet transforms (including wavelet packets). This approach gives the user more flexibility in applying wavelets to study multidimensional data sets.
Spline wavelets with uniform or arbitrary knots on a bounded interval (with methods to construct these wavelets, their duals, as well as all decomposition and reconstruction matrices). This tool allows analysis and synthesis of discrete data on uniform or nonuniform sample sites without any boundary effect.
Wavelets as a mathematical tool for waveform matching, signal segmentation, and time-frequency localization as well as effective implementation and fast computation.
Procedures to construct all the well-known wavelets and to find their corresponding filter sequences.
Detailed comparisons of the most popular wavelets and tables of values for evaluating their filtering performance.

Contents

Foreword
Preface
Software
Notation
Chapter 1: What are wavelets? Waveform modeling and segmentation
Time-frequency analysis
Fast algorithms and filter banks
Chapter 2: Time-Frequency Localization. Analog filters
RMS bandwidths
The short-time Fourier transform
The integral wavelet transform
Modeling the cochlea
Chapter 3: Multiresolution Analysis. Signal spaces with finite RMS bandwidth
Two simple mathematical representations
Multiresolution analysis
Cardinal splines
Chapter 4: Orthonormal Wavelets. Orthogonal wavelet spaces
Wavelets of Haar, Shannon, and Meyer
Spline wavelets of Battle-Lemarié and Strömberg
The Daubechies wavelets
Chapter 5: Biorthogonal Wavelets. The need for duals
Compactly supported spline wavelets
The duality principle
Total positivity and optimality of time-frequency windows
Chapter 6: Algorithms. Signal representations
Orthogonal decompositions and reconstructions
Graphical display of signal representations
Multidimensional wavelet transforms
The need for boundary wavelets
Spline functions on a bounded interval
Boundary spline wavelets with arbitrary knots
Chapter 7: Applications. Detection of singularities and feature extraction
Data compression
Numerical solutions of integral equations
Summary and Notes
References
Subject Index.