Introduction to Wavelet Transforms

This book introduces the basics of wavelet transforms, including continuous and discrete wavelet transforms, and Daubechies wavelets. It also includes elementary examples of wavelets, and certain well-known applications.

The textbook, Introduction to Wavelet Transforms provides basics of wavelet transforms in a self-contained manner. Applications of wavelet transform theory permeate our daily lives. Therefore it is imperative to have a strong foundation for this subject.

Features

• No prior knowledge of the subject is assumed. Sufficient mathematical background is provided to complete the discussion of different topics.

• Different topics have been properly segmented for easy learning. This makes the textbook pedagogical and unique.

• Notation is generally introduced in the definitions. Relatively easy consequences of the definitions are listed as observations, and important results are stated as theorems.

• Examples are provided for clarity and to enhance reader's understanding of the subject.

• Each chapter also has a problem section. A majority of the problems are provided with sufficient hints.

The textbook can be used either in an upper-level undergraduate or first-year graduate class in electrical engineering, or computer science, or applied mathematics. It can also be used by professionals and researchers in the field who would like a quick review of the basics of the subject.

About the Author

Nirdosh Bhatnagar works in both academia and industry in Silicon Valley, California. He is also the author of a comprehensive two-volume work: Mathematical Principles of the Internet, published by the CRC Press in the year 2019. Nirdosh earned M.S. in Operations Research, and M.S. and Ph.D. in electrical engineering, all from Stanford University, Stanford, California.

Autorentext

Nirdosh Bhatnagar works, both in the academia and industry in Silicon Valley, California, USA. He is the author of several papers and reports. Nirdosh earned an MS in operations research, and MS and PhD in electrical engineering, all from Stanford University, Stanford, California.

Klappentext

The textbook, Introduction to Wavelet Transforms provides basics of wavelet transforms in a self-contained manner. Applications of wavelet transform theory permeate our daily lives. Therefore it is imperative to have a strong foundation for this subject. Features No prior knowledge of the subject is assumed. Sufficient mathematical background is provided to complete the discussion of different topics. Different topics have been properly segmented for easy learning. This makes the textbook pedagogical and unique. Notation is generally introduced in the definitions. Relatively easy consequences of the definitions are listed as observations, and important results are stated as theorems. Examples are provided for clarity and to enhance reader's understanding of the subject. Each chapter also has a problem section. A majority of the problems are provided with sufficient hints. The textbook can be used either in an upper-level undergraduate or first-year graduate class in electrical engineering, or computer science, or applied mathematics. It can also be used by professionals and researchers in the field who would like a quick review of the basics of the subject. About the Author Nirdosh Bhatnagar works in both academia and industry in Silicon Valley, California. He is also the author of a comprehensive two-volume work: Mathematical Principles of the Internet, published by the CRC Press in the year 2019. Nirdosh earned M.S. in Operations Research, and M.S. and Ph.D. in electrical engineering, all from Stanford University, Stanford, California.

Inhalt

Table of Contents

Preface

List of Symbols

Greek Symbols

Part I. Basics of Wavelet Transforms.

Introduction to Wavelets

Continuous Wavelet Transform

Discrete Wavelet Transform

Daubechies Wavelets

Some Examples of Wavelets.

Applications

Part II. Intermediate Topics.

Periodic Wavelet Transform

Biorthogonal Wavelet Transform

Coiflets

The Lifting Technique

Wavelet Packets

Lapped Orthogonal Transform.

Part III. Signal Processing.

Discrete Fourier Transform

The z-Transform and Discrete-Time Fourier Transform

Elements of Continuous-Time Signal Processing

Elements of Discrete-Time Signal Processing

Part IV. Mathematical Concepts

Set-Theoretic Concepts and Number Theory

Matrices and Determinants

Applied Analysis

Fourier Theory

Probability Theory and Stochastic Processes

References

Index