ABSTRACT

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.

part I|128 pages

Basics of Wavelet Transforms

chapter Chapter 1|12 pages

Introduction to Wavelets

chapter Chapter 2|10 pages

Continuous Wavelet Transform

chapter Chapter 3|30 pages

Discrete Wavelet Transform

chapter Chapter 4|27 pages

Daubechies Wavelets

chapter Chapter 5|23 pages

Some Examples of Wavelets

chapter Chapter 6|22 pages

Applications

part II|147 pages

Intermediate Topics

chapter Chapter 7|19 pages

Periodic Wavelet Transform

chapter Chapter 8|27 pages

Biorthogonal Wavelet Transform

chapter Chapter 9|11 pages

Coiflets

chapter Chapter 10|28 pages

The Lifting Technique

chapter Chapter 11|20 pages

Wavelet Packets

chapter Chapter 12|37 pages

Lapped Orthogonal Transform

part III|47 pages

Signal Processing

chapter Chapter 13|13 pages

Discrete Fourier Transform

chapter Chapter 14|8 pages

The z-Transform and Discrete-Time Fourier Transform

chapter Chapter 15|6 pages

Elements of Continuous-Time Signal Processing

chapter Chapter 16|17 pages

Elements of Discrete-Time Signal Processing

part IV|113 pages

Mathematical Concepts

chapter Chapter 17|15 pages

Set-Theoretic Concepts and Number Theory

chapter Chapter 18|12 pages

Matrices and Determinants

chapter Chapter 19|41 pages

Applied Analysis

chapter Chapter 20|23 pages

Fourier Theory

chapter Chapter 21|17 pages

Probability Theory and Stochastic Processes