Meet the editor

Dr. Somayeh Mohammady obtained a Ph.D. in Electrical and Electronic Engineering in 2012 from University Putra Malaysia (UPM). Prior to her current work as a certified lecturer, researcher, and publisher at the Technological University of Dublin (TU Dublin), she worked as a postdoc fellow and design engineer. Dr. Mohammady's research interests include digital signal processing (DSP), power efficiency improvement algorithms in

wireless telecommunication systems, physical layer security improvement, bandpass filter design using optimization algorithms, the Internet of Things (IoT), and robotics and programmable logic control (PLC) automation systems. Her hobbies include illustrating, yoga, and swimming. She is skilled in communications, Arduino, and Allen-Bradley automation equipment. She is actively engaged in gender equality in Science, Technology, Engineering, and Mathematics (STEM) activities.

Contents

**Section 1**

**Section 2**

Signal Processing

PAPR Analysis

*by Nikesh Bajaj*

Wavelet Transforms

**Section 3**

*by Karlton Wirsing*

*and Zahrah Ismael Salman*

*and Sumesh Eratt Parameswaran*

Wavelets for EEG Analysis

*Safa Saadaoui and Abbas Dandache*

**Preface V**

Wavelet Algorithm and Overview **1**

**Chapter 1 3**

**Chapter 2 21**

Wavelet Theory and Communication Systems **43**

**Chapter 3 45**

**Chapter 4 63**

Signal Processing and Wavelet Theory **87**

**Chapter 5 89**

**Chapter 6 105**

Ultra-High Performance and Low-Cost Architecture of Discrete

*by Mouhamad Chehaitly, Mohamed Tabaa, Fabrice Monteiro,*

Time Frequency Analysis of Wavelet and Fourier Transform

Wavelet Theory and Application in Communication and

Wavelet Based Multicarrier Modulation (MCM) Systems:

*by Jamaluddin Zakaria and Mohd Fadzli Mohd Salleh*

*by Nizar Al Bassam, Vidhyalavanya Ramachandran*

Wavelet Theory: Applications of the Wavelet *by Mohammed S. Mechee, Zahir M. Hussain*

## Contents



**Chapter 16 349**

**Chapter 17 369**

Higher Order Haar Wavelet Method for Solving Differential

*by Jüri Majak, Mart Ratas, Kristo Karjust and Boris Shvartsman*

COVID-19 Outbreak and Co-Movement of Global Markets: Insight from Dynamic Wavelet Correlation Analysis *by Maurice Omane-Adjepong, Imhotep Paul Alagidede*

Equations

*and John Bosco Dramani*

**Chapter 16 349** Higher Order Haar Wavelet Method for Solving Differential Equations *by Jüri Majak, Mart Ratas, Kristo Karjust and Boris Shvartsman*

#### **Chapter 17 369**

**Chapter 7 123**

Wavelet Theory and Internet of Things (IoT) **161**

**Chapter 8 163**

**Chapter 9 183**

Wavelet Transform and Computations **203**

**Chapter 10 205**

**Chapter 11 231**

**Chapter 12 263**

**Chapter 13 289**

Recent Applications of Wavelet Theory **309**

**Chapter 14 311**

**Chapter 15 333**

Fault Detection, Diagnosis, and Isolation Strategy in Li-Ion Battery Management Systems of HEVs Using 1-D Wavelet Signal Analysis

*by Nicolae Tudoroiu, Mohammed Zaheeruddin, Roxana-Elena Tudoroiu and Sorin Mihai Radu*

Industrial IoT Using Wavelet Transform

Wavelet Transform for Signal Processing in

The Discrete Quincunx Wavelet Packet Transform

Uncertainty and the Oracle of Market Returns: Evidence from

Case Study: Coefficient Training in Paley-Wiener Space, FFT, and

A Wavelet Threshold Function for Treatment of Partial Discharge

*by Caio F.F.C. Cunha, Mariane R. Petraglia, André T. Carvalho*

Use of Daubechies Wavelets in the Representation of Analytical

*by Indrakshi Dey and Shama Siddiqui*

Internet-of-Things (IoT)

*by Abdesselam Bassou*

Wavelet Theory

*by Xi Zhang*

**Section 6**

Measurements

Functions

**II**

*and Antonio C.S. Lima*

*by Paulo César Linhares da Silva*

Wavelet Coherence Analysis *by Joan Nix and Bruce D. McNevin*

*by Kayupe Kikodio Patrick*

Wavelet Filter Banks Using Allpass Filters

*by Mohamed Tabaa, Safa Saadaoui, Mouhamad Chehaitly, Aamre Khalil, Fabrice Monteiro and Abbas Dandache*

**Section 4**

**Section 5**

COVID-19 Outbreak and Co-Movement of Global Markets: Insight from Dynamic Wavelet Correlation Analysis *by Maurice Omane-Adjepong, Imhotep Paul Alagidede and John Bosco Dramani*

Preface

A wavelet is an important mathematical tool that appears in many fields of science and technology. It refers to analyzing data with special features and different scales

The name "wavelet" first appeared in the early 1980s. It comes from the French word "ondelette," meaning "small wave." The original idea is rooted in many separate thoughts including Jean-Baptiste Joseph Fourier and his theory of approximation in which a complex function can be approximated as a weighted sum of simpler functions, Alfréd Haar and his theory of a sequence of rescaled "squareshaped" functions, and Dennis Gabor and his function for minimizing the deviation

The application of wavelet theory is rapidly growing in diverse fields and disciplines. As such, this book examines some of the most creative and popular applications including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic

My personal interest in wavelet theory lies in its features, which are in contrast to Fourier transform, and its application in converting time domain signals to frequency domain signals and vice versa. The wavelet transform (WT) identifies what frequencies are present in a signal as well as when the signal experiences changes in the time domain, and thus the wavelet has information about where, what scale, and when the change occurred. This makes it very interesting for the study of high peaks in the time domain, which causes distortions in the frequency domain.

The mentioned research topics are also known as peak to average power ratio (PAPR) reduction or crest factor reduction (CRF) techniques. Any improvement of time domain peaks is directly related to the power efficiency of the amplification stage of telecommunication systems. Therefore, the study of the nonlinear behavior and distortion in high power amplifiers (HPA) is relative to the use of wavelets in this field. These topics are relevant to existing and future wireless telecommunica-

I would like to thank all my family and friends for their encouragement and support. I also acknowledge that this publication is associated with CONNECT - the Science Foundation Ireland Research Centre for Future Networks and Communications.

**Somayeh, Mohammady**

Dublin, Republic of Ireland

School of Electrical and Electronic Engineering, Technological University Dublin (TU Dublin),

depending on the application requirements.

in the time and frequency domains.

measurements and calculations.

tion systems such as 5G and beyond.
