Meet the editors

Goran S. Nikolić was born on 1 November 1966 in Knez Selo (Niš, Serbia). He received his PhD degree in Chemical Engineering from the University of Niš (2001). Currently, he is a full professor for the pharmaceutical engineering group of subjects at the Faculty of Technology in Leskovac. His research activities are applied spectroscopy and quality control of drugs. He has experience in project management and managing academic insti-

tutions at different levels. He is a member of several Serbian projects in the technological development area, and member of numerous TEMPUS European projects of sustainable technologies and management courses. He has authored more than 300 scientific papers (h-index 16), numerous technological solutions for industry, monographs, patents, university textbooks, and invitation lecturers. He is the referee in numerous international journals and the editor of four Books on Fourier Transform (IntechOpen).

Dragana Z. Marković-Nikolić was born on 28 December 1982 in Leskovac (Serbia). She received her PhD degree in Applied Chemistry from the University of Niš (2018). She was elected as a teaching assistant at the High Technologically Artistic Professional School in Leskovac (2011), where she is still working. She is intensively engaged in scientific research in the field of ecological engineering. She has published her research results in

numerous scientific journals and presented at scientific meetings. She is the author of several technological solutions for industry, practical textbooks, and book chapters (IntechOpen). As an expert associate (2016), she acquired practical knowledge and skills for the application of contemporary instrumental and analytical methods, as well as skills for scientific research in the field of ecological engineering. She participated in the realization of the TEMPUS project titled "Creation of University-Enterprise Cooperation for Education on Sustainable Technologies". She is a member of the Chemical Society of Serbia.

Contents

The Discrete Hankel Transform

*by Natalie Baddour*

Networks

**Preface III**

**Chapter 1 1**

**Chapter 2 25**

**Chapter 3 39**

**Chapter 4 57**

**Chapter 5 75**

**Chapter 6 93**

**Chapter 7 107**

**Chapter 8 123**

Analysis of Financial Time Series in Frequency Domain Using Neural

Establishment of FTIR Database of Roselle Raw Material Originated

Application of Fourier Analysis of Cerebral Glucose Metabolism in Color-Induced Long-Term Potentiation: A Novel Functional PET

*by Choong Yew Keong, Nor Syaidatul Akmal Mohd Yousof, Jamia Azdina Jamal* 

Fourier Transforms for Generalized Fredholm Equations

*Alejandro Perez Ricardez and Jaime Granados Samaniego*

The RR Interval Spectrum, the ECG Signal, and Aliasing *by Alexander Gersten, Ori Gersten, Adi Ronen and Yair Cassuto*

Directional Denoising Using Fourier Spectrum Cloning

*by Laurent Navarro and Jérôme Molimard*

Fourier Transform in Ultrafast Spectroscopy

From Western Coastline in Peninsular Malaysia

*by Philip C. Njemanze, Mathias Kranz and Peter Brust*

Spectroscopy ( *f* PETS) Study in Mice

*by Stefan Nikolić and Goran Nikolić*

*by Adrien A.P. Chauvet*

*and Mohd Isa Wasiman*

*by Juan Manuel Velazquez Arcos, Ricardo Teodoro Paez Hernandez,* 

## Contents


Preface

*"The fact is that Gutenberg led to books being put in shelves, and digitisation is taking books off shelves. If you start taking books off shelves then you are only going to find what you are looking for, which does not help those who do not know what* 

Modern technologies surround all of us and they are our most reliable partners for the future. The 21st century ushered in a new era of technology that has been reshaping everyday life, simplifying outdated processes, and even giving rise to entirely new business sectors. On the other hand, contemporary customers and users of products and services expect more and more personalized products and services that can meet their unique needs. Through good-quality work and determination, clients will share with you their business needs and requirements, certain that you will find the right solutions for them. Therefore, companies must continuously improve their competitiveness and explore modern ways and techniques for the full experience of clients. For this, it is necessary to further develop existing methods, adapt them to new applications, or the discovering of new methods.

Methods that have an increasing impact on humanity today and can solve different types of problems even in specific industries are: artificial intelligence, neural networks, machine learning, digital signal processing, spectroscopy, process optimization, methods for analyzing and predicting financial markets, time series analysis etc. Upgrading with Fourier Transformation gives a different meaning to the method. Methods based on Fourier Transformation have great application in all areas of science and engineering. New technologies support their development and have good projected acceleration in the future. The future has five faces: Innovation, Digitalization, Urbanization, Community, and Humanity. The scientific sector should develop each of these faces, but one that occupies a leading position is definitely Digitalization. Digitalization is transforming our industry and making it more efficient and customer-centric than ever before. It strives for the future every

This book provides a detailed overview of some Fourier Transformation based methods that have an increasing impact on humanity and can solve different types

The first chapter presents a mathematical theory of a Discrete Hankel Transform (DHT) that is shown to arise from a discretization scheme based on the theory of Fourier–Bessel expansions. The Hankel Transform (HT), also known as the Fourier-Bessel Transform, is a significant integral transform that has been applied in many areas of science and engineering. HT is closely related to the Fourier Transform (HT of 0th order is a 2D FT of a rotationally symmetric function, HT appears in defining the 2D FT in polar coordinates and the spherical, as well as in the definition of the 3D FT in spherical polar coordinates). The scientific contribution of this chapter is to present the theory of DHT as a 'stand-alone' transformation. The author has

day and is struggling to overcome professional challenges.

of problems.

*- Jeanette Winterson*

*they are looking for."*
