Preface

Chapter 7 **Application of Wavelet Decomposition and Phase Space**

Chapter 8 **Wavelet Transform for Educational Network Data Traffic**

Chapter 9 **The 2D Continuous Wavelet Transform: Applications in Fringe**

José de Jesús Villa Hernández, Ismael de la Rosa, Gustavo Rodríguez, Jorge Luis Flores, Rumen Ivanov, Guillermo García,

**Pattern Processing for Optical Measurement Techniques 173**

Yossef Ben Ezra, Boris I. Lembrikov, Moshe Schwartz and Segev

Edwin Muchebve, Yoshiyuki Nakamura and Hiroshi Kamiya

**Chaotic Approach (Case Study) 131**

**Analysis 155**

**VI** Contents

Shwan Dyllon and Perry Xiao

Daniel Alaniz and Efrén González

**Dynamics in Coastal Lakes 215**

Chapter 12 **Wavelets and LPG-PCA for Image Denoising 237** Mourad Talbi and Med Salim Bouhlel

**Superoscillations 195**

Zarkovsky

Chapter 10 **Applications of Wavelet Transforms to the Analysis of**

Chapter 11 **Use of Wavelet Techniques in the Study of Seawater Flux**

**Reconstruction in Urban Water Consumption Forecasting:**

Peyman Yousefi, Gholamreza Naser and Hadi Mohammadi

The concept of wavelets is quite new and different to the readers. Original research works were carried out in the field of mathematics, electrical engineering, physics, applied science, and engineering such as geophysics and finance.

A wavelet is a wavelike oscillation with amplitude that begins at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like the one re‐ corded by a heart monitoring system. Generally, wavelets have specific properties that make them useful for signal processing application.

Wavelet theory is applicable to several areas. Wavelet transforms normally come with timefrequency representation for analog signals. For any practical purpose, people use discrete wavelet transforms, which use discrete-time filter banks for implementation. These filter banks are called the wavelet and scaling coefficients in wavelet nomenclature. These filter banks may contain either finite impulse response (FIR) or infinite impulse response (IIR) fil‐ ters. To understand these filters, signal processing concepts are very much essential.

**Scope of the book:** This book is the research outcome of various researchers and professors who have contributed a lot in applying wavelets in different application areas. This book suits researchers doing their research in the area of wavelets and its applications. The under‐ standing of fundamentals of linear algebra and signal processing concepts is essential for the readers before reading this book. This book gives fundamental idea of wavelets and also how wavelets can be applied in different fields such as biomedical, prediction analysis, and finance. I do not have any doubts that this book will motivate researchers in different parts of the world to use the concepts, which are available in this book for their research.

**Structure of the book:** The book contains 12 chapters grouped into four sections. The reader of the book is expected to know the fundamentals of linear algebra and signal processing, which are available in the standard books. The book starts with an introductory chapter. Section 2 deals with the role of wavelets in biomedical application containing three chapters. Section 3 describes how wavelets can be applied in the field of finance containing two chap‐ ters. Section 4 concentrates on the usage of wavelets in contemporary applications contain‐ ing seven chapters.

#### **Acknowledgment**

I thank the Almighty for showering blessings and giving me intelligence and energy to com‐ plete this work. I thank all the professors and scientists who have contributed to the differ‐ ent chapters. My sincere thanks go to the management of Dr. Mahalingam College of Engineering and Technology and Prof. C. Ramaswamy, Secretary, NIA Institutions, for their encouragement and patronage rendered to carry out this work. I am indebted to my wife

Mrs. Vinitha Mohan. Her support, encouragement, quiet patience, and unwavering love un‐ deniably led me to the successful completion of the work. I have no words to thank my son S.V. Hemesh for bearing my preoccupation, understanding, and love he gave me. I am grateful to the IntechOpen publishing team specially Mr. Markus Mattila, Publishing Proc‐ ess Manager, who constantly helped me in bringing out this book.

> **Dr. R. Sudhakar** Professor, Department of Electronics and Communication Engineering Dr. Mahalingam College of Engineering and Technology India

**Section 1**

**Introduction**

**Section 1**
