Preface

The wavelet transform is a powerful method applied with great success in several disciplines. For example, when we decompose a signal into wavelets rather than frequencies we can obtain a much better resolution in the domain it is transformed into. Alternatively, when we use a specific wavelet transform the signal is transformed into the wavelet domain. The existence of several wavelet families is a great advantage of the method; however, the question of which is the best family to treat a given data still remains.

This book is structured into two main parts: Analysis and Real-World Applications.

Chapters in Part 1 include: "Using Wavelets for Gait and Arm Swing Analysis" by Yor Jaggy Castaño-Pino, Andrés Navarro, Beatriz Muñoz, and Jorge Luis Orozco; "Analysis of Wavelet Transform Design via Filter Bank Technique" by Peter Yusuf Dibal, Elizabeth Onwuka, James Agajo, and Caroline Alenoghena; and "Wavelets for Differential Equations and Numerical Operator Calculus" by Riccardo Bernardini.

Chapters in Part 2 include: "DWT-Based Data Hiding Technique for Videos Ownership Protection" by Farhan A. Alenizi and Awad Kh. Al-Asmari; "Wavelet Transform Analysis to Applications in Electric Power Systems" by Mario O. Oliveira, J. H. Reversat, and Lucas A. Reynoso; and "Wavelet Transform Applied to Internal Defect Detection by Means of LASER Ultrasound" by Hossam Selim, Fernando Piñal Moctezuma, Miguel Delgado Prieto, José Francisco Trull, Luis Romeral Martínez, and Crina Cojocaru.

The book is designed for students, postdocs, and researchers willing to enter or to go further into the fascinating world of wavelet theory and its applications.

### **Dumitru Baleanu**

Professor, Institute of Space Sciences, Magurele, Bucharest, Romania

Department of Mathematics, Faculty of Arts and Sciences, Ankara, Turkey

**1**

Section 1

Analysis

Section 1 Analysis

**3**

**Chapter 1**

**Abstract**

Swing Analysis

*and Jorge Luis Orozco*

spatiotemporal variables

**1. Introduction**

affected elderly.

Using Wavelets for Gait and Arm

*Yor Jaggy Castaño-Pino, Andrés Navarro, Beatriz Muñoz* 

The human walking pattern can be affected by different factors such as accidents,

Aging is associated with numerous physiological problems that affect the brain. Some of these problems occur in the context of aging, such as cognitive deterioration and motor involvement, and often have an important impact on the central nervous system [1]. The causes of these deficits can be multifactorial and involve the central nervous system, the sensory receptors, the muscles, and the peripheral nerves [2]. On the other hand, there are comorbidities such as Parkinson's disease that can generate an even more marked deterioration of the motor skills of the

Parkinson's disease (PD) is a neurodegenerative disease that mainly affects people older than 60 years and is characterized by a neuronal loss in several areas and brain nuclei, but particularly in the substantia nigra, which can lead initially to motor alterations and delayed cognitive disorders that condition the patient to present physical dependence toward the caregiver and commitment to their autonomy [3]. Among the alterations mentioned are those associated with walking and arm swing. The march and its spatiotemporal characteristics have been analyzed since the Renaissance, and currently the analysis of this has become a very useful tool in the diagnostic evaluation and the severity of the disease, the response to treatment, as well as the impact of therapeutic interventions which can additionally predict the risk of falls [4]. Quantitative gait studies have usually focused on the characteristics of each participant and on the average of steps ignoring the step-by-step fluctuations

transplants, or diseases, like Parkinson's disease, which affects motor and mental functions. In motor terms, this disease can generate alterations such as tremors, festination, rigidity, unbalance, slowness, and freezing of gait. Additionally, it is estimated that for the year 2040, the number of people with Parkinson's in the world will be between 12.9 and 14.2 million people. These alarming figures make Parkinson's disease an important focus of attention. In this chapter, we present contributions that suggest wavelet techniques as a useful tool to perform a gait and arm swing analysis; this represents an important approximation that can contribute to describe and differentiate people with Parkinson's disease in early stages of the disease.

**Keywords:** wavelet, gait analysis, arm swing, Parkinson diagnose,
