Fractal Functions Dimensions And Signal Analysis PDF Download

Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Fractal Functions Dimensions And Signal Analysis PDF full book. Access full book title Fractal Functions Dimensions And Signal Analysis.

Fractal Functions, Dimensions and Signal Analysis

Fractal Functions, Dimensions and Signal Analysis
Author: Santo Banerjee
Publisher: Springer Nature
Total Pages: 132
Release: 2020-12-14
Genre: Science
ISBN: 3030626725
GET BOOK

Download Fractal Functions, Dimensions and Signal Analysis Book in PDF, ePub and Kindle

This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the countable iterated function system is demonstrated by taking suitable monotone and bounded sequences. It also covers the dimension of fractal functions and investigates the relationship between the fractal dimension and the fractional order of fractal interpolation functions. Moreover, this book explores the idea of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the problems of identification of the characterizing parameters. In the application section, this research compendium addresses the signal processing and its Mathematical methodologies. A wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals contaminated by nonstationary noises is presented, and the author investigates the recognition of healthy, epileptic EEG and cardiac ECG signals using multifractal measures. This book is intended for professionals in the field of Mathematics, Physics and Computer Science, helping them broaden their understanding of fractal functions and dimensions, while also providing the illustrative experimental applications for researchers in biomedicine and neuroscience.

Fractal Functions, Dimensions and Signal Analysis: Fractal functions.-Chapter 3. Fractional calculus and generalized fractal functions

Fractal Functions, Dimensions and Signal Analysis: Fractal functions.-Chapter 3. Fractional calculus and generalized fractal functions
Author: Santo Banerjee
Publisher:
Total Pages: 0
Release: 2021
Genre:
ISBN: 9783030626730
GET BOOK

Download Fractal Functions, Dimensions and Signal Analysis: Fractal functions.-Chapter 3. Fractional calculus and generalized fractal functions Book in PDF, ePub and Kindle

This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the countable iterated function system is demonstrated by taking suitable monotone and bounded sequences. It also covers the dimension of fractal functions and investigates the relationship between the fractal dimension and the fractional order of fractal interpolation functions. Moreover, this book explores the idea of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the problems of identification of the characterizing parameters. In the application section, this research compendium addresses the signal processing and its Mathematical methodologies. A wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals contaminated by nonstationary noises is presented, and the author investigates the recognition of healthy, epileptic EEG and cardiac ECG signals using multifractal measures. This book is intended for professionals in the field of Mathematics, Physics and Computer Science, helping them broaden their understanding of fractal functions and dimensions, while also providing the illustrative experimental applications for researchers in biomedicine and neuroscience.

Frontiers of Fractal Analysis

Frontiers of Fractal Analysis
Author: Santo Banerjee
Publisher: CRC Press
Total Pages: 182
Release: 2022-07-07
Genre: Mathematics
ISBN: 1000625877
GET BOOK

Download Frontiers of Fractal Analysis Book in PDF, ePub and Kindle

The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.

Fractal Geometry in Digital Imaging

Fractal Geometry in Digital Imaging
Author: Martin J. Turner
Publisher: Academic Press
Total Pages: 352
Release: 1998-06-23
Genre: Computers
ISBN: 9780127039701
GET BOOK

Download Fractal Geometry in Digital Imaging Book in PDF, ePub and Kindle

This book is concerned with the theory and application of fractal geometry in digital imaging. Throughout the book, a series of new approaches to defining fractals are illustrated, such as the analysis of the fractal power spectrum and the use of fractional differentials. Several new algorithms and applications are also discussed and applied to real life images. Fractal Geometry in Digital imaging will appeal to postgraduates, researchers and practitioners in image processing, mathematics and computing, information technology and engineering.

Fractal Functions, Fractal Surfaces, and Wavelets

Fractal Functions, Fractal Surfaces, and Wavelets
Author: Peter R. Massopust
Publisher: Academic Press
Total Pages: 428
Release: 2016-09-02
Genre: Mathematics
ISBN: 0128044705
GET BOOK

Download Fractal Functions, Fractal Surfaces, and Wavelets Book in PDF, ePub and Kindle

Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust’s work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content. Offers a comprehensive presentation of fractal functions and fractal surfaces Includes latest developments in fractal interpolation Connects fractal geometry with wavelet theory Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet sets Deepens and extends the pedagogical content

Fractals in Engineering

Fractals in Engineering
Author: Jacques Levy Vehel
Publisher: Springer Science & Business Media
Total Pages: 408
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1447109953
GET BOOK

Download Fractals in Engineering Book in PDF, ePub and Kindle

Fractal analysis research is expanding into a variety of engineering domains. The strong potential of this work is now beginning to be seen in important applications in real industrial situations. Recent research progress has already led to new developments in domains such as signal processing and chemical engineering, and the major advances in fractal theory that underlie such developments are detailed here. New domains of applications are also presented, among them environmental science and rough surface analysis. Sections include multifractal analysis, iterated function systems, random processes, network traffic analysis, fractals and waves, image compression, and applications in physics. Fractals in Engineering emphasizes the connection between fractal analysis research and applications to industry. It is an important volume that illustrates the scientific and industrial value of this exciting field.

Fractals: Theory and Applications in Engineering

Fractals: Theory and Applications in Engineering
Author: Michel Dekking
Publisher: Springer Science & Business Media
Total Pages: 336
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1447108736
GET BOOK

Download Fractals: Theory and Applications in Engineering Book in PDF, ePub and Kindle

Owing to the rapid emergence and growth of techniques in the engineering application of fractals, it has become necessary to gather the most recent advances on a regular basis. This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more involved in the definition and use of fractal models. It seems that the time of the qualitative observation of fractal phenomena has gone. Now the main models are strongly based upon theoretical arguments. Fractals: Theory and Applications in Engineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.

Applied Analysis, Optimization and Soft Computing

Applied Analysis, Optimization and Soft Computing
Author: Tanmoy Som
Publisher: Springer Nature
Total Pages: 425
Release: 2023-06-10
Genre: Mathematics
ISBN: 9819905974
GET BOOK

Download Applied Analysis, Optimization and Soft Computing Book in PDF, ePub and Kindle

This book contains select contributions presented at the International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), held at the Department of Mathematics Sciences, Indian Institute of Technology (BHU) Varanasi, India, from 21–23 December 2021. The book discusses topics in the areas of nonlinear analysis, fixed point theory, dynamical systems, optimization, fractals, applications to differential/integral equations, signal and image processing, and soft computing, and exposes the young talents with the newer dimensions in these areas with their practical approaches and to tackle the real-life problems in engineering, medical and social sciences. Scientists from the U.S.A., Austria, France, Mexico, Romania, and India have contributed their research. All the submissions are peer reviewed by experts in their fields.

Fractal Analysis

Fractal Analysis
Author: Fernando Brambila
Publisher: BoD – Books on Demand
Total Pages: 228
Release: 2017-07-26
Genre: Medical
ISBN: 953513213X
GET BOOK

Download Fractal Analysis Book in PDF, ePub and Kindle

Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book. Here we present the use of fractal geometry, in particular, fractal analysis in two sciences: health sciences and social sciences and humanities. Part 1 is Health Science. In it, we present the latest advances in cardiovascular signs, kidney images to determine cancer growth, EEG signals, magnetoencephalography signals, and photosensitive epilepsy. We show how it is possible to produce ultrasonic lenses or even sound focusing. In Part 2, we present the use of fractal analysis in social sciences and humanities. It includes anthropology, hierarchical scaling, human settlements, language, fractal dimension of different cultures, cultural traits, and Mesoamerican complexity. And in Part 3, we present a few useful tools for fractal analysis, such as graphs and correlation, self-affine and self-similar graphs, and correlation function. It is impossible to picture today's research without fractal geometry.

Applied Fractional Calculus in Identification and Control

Applied Fractional Calculus in Identification and Control
Author: Utkal Mehta
Publisher: Springer Nature
Total Pages: 212
Release: 2022-09-10
Genre: Technology & Engineering
ISBN: 9811935017
GET BOOK

Download Applied Fractional Calculus in Identification and Control Book in PDF, ePub and Kindle

The book investigates the fractional calculus-based approaches and their benefits to adopting in complex real-time areas. Another objective is to provide initial solutions for new areas where fractional theory has yet to verify the expertise. The book focuses on the latest scientific interest and illustrates the basic idea of general fractional calculus with MATLAB codes. This book is ideal for researchers working on fractional calculus theory both in simulation and hardware. Researchers from academia and industry working or starting research in applied fractional calculus methods will find the book most useful. The scope of this book covers most of the theoretical and practical studies on linear and nonlinear systems using fractional-order integro-differential operators.