Overview
- Focuses on the fundamentals of fractional calculus of fractal functions in various settings, and its applications in signal analysis
- Covers thoroughly the generalized fractal dimensions and the discrete wavelet transform for analyzing EEG signals
- Discusses the fuzzy multifractal dimensions for analyzing the mathematical and clinical waveforms
Part of the book series: Understanding Complex Systems (UCS)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the authors
Santo Banerjee was working as Associate Professor, in the Institute for Mathematical Research (INSPEM), University Putra Malaysia, Malaysia till 2020, and also a founder member of the Malaysia-Italy Centre of Excellence in Mathematical Science, UPM, Malaysia. He is now associated with the Department of Mathematics, Politecnico di Torino, Italy. His research is mainly concerned with Nonlinear Dynamics, Chaos, Complexity and Secure Communication. He is a Managing Editor of EPJ Plus (Springer)
D. Easwaramoorthy received the M.Sc. Degree in Mathematics from the Bharathidasan University, Tiruchirappalli, India in 2008 and the Ph.D. Degree in Mathematics from The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Dindigul, India in 2013. Currently, he is an Assistant Professor (Senior) in the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (Deemed to be University), Vellore, Tamil Nadu, India. His research interests include Fractal Analysis, Fuzzy Metric Spaces, Fuzzy Mathematics, Signal & Image Analysis; and Biomedical Signal Analysis.A. Gowrisankar received the M.Sc. and Ph.D. Degrees in Mathematics from the The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Dindigul, India in 2012 and 2017 respectively. He got institute postdoctoral fellowship from Indian Institute of Technology Guwahati (IITG), Guwahati, Assam, India in 2017. At present, he is an Assistant Professor in the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (Deemed to be University), Vellore, Tamil Nadu, India. His broad area of research includes Fractal Analysis, Image Processing, Fractional Calculus and Fractal Functions.
Bibliographic Information
Book Title: Fractal Functions, Dimensions and Signal Analysis
Authors: Santo Banerjee, D. Easwaramoorthy, A. Gowrisankar
Series Title: Understanding Complex Systems
DOI: https://doi.org/10.1007/978-3-030-62672-3
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-62671-6Published: 15 December 2020
Softcover ISBN: 978-3-030-62674-7Published: 16 December 2021
eBook ISBN: 978-3-030-62672-3Published: 14 December 2020
Series ISSN: 1860-0832
Series E-ISSN: 1860-0840
Edition Number: 1
Number of Pages: X, 132
Number of Illustrations: 2 b/w illustrations, 59 illustrations in colour
Topics: Applications of Nonlinear Dynamics and Chaos Theory, Complexity, Complex Systems