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.
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
Biography
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.
