A. Gowrisankar's Books

Fractal Functions, Dimensions and Signal Analysis

By: Santo Banerjee,D. Easwaramoorthy,A. Gowrisankar

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Fractal Functions, Dimensions and Signal Analysis

By: Santo Banerjee,D. Easwaramoorthy,A. Gowrisankar

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.

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Page Count

132

Publisher

Springer Nature

Published Date

ISBN 10

3030626725

ISBN 13

9783030626723

Fractal Patterns with MATLAB

By: Santo Banerjee,A. Gowrisankar,Komandla Mahipal Reddy

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Fractal Patterns with MATLAB

By: Santo Banerjee,A. Gowrisankar,Komandla Mahipal Reddy

This book presents the iterative beauty of fractals and fractal functions graphically with the aid of MATLAB programming. The fractal images generated using the MATLAB codes provide visual delight and highly encourage the fractal lovers for creative thinking. The book compiles five cutting-edge research chapters, each with state-of-the art fractal illustrations. It starts with the fundamental theory for the construction of fractal sets via the deterministic iteration algorithm. Incorporating the theoretical base, fractal illustrations of elementary fractal sets are provided with the explicit MATLAB code. The book gives examples of MATLAB codes to present the fractal surfaces. This book is contributed to all the research beginners as well as the professionals on the field of fractal analysis. As it covers basic fractals like Sierpinski triangle to advanced fractal functions with explicit MATLAB code, the presented fractal illustrations hopefully benefit even the non-field readers. The book is a useful course to all the research beginners on the fractal and fractal-related fields.

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Publisher

Springer Nature

Published Date

ISBN 10

303148102X

ISBN 13

9783031481024

Fractal Patterns in Nonlinear Dynamics and Applications

By: Santo Banerjee,M K Hassan,Sayan Mukherjee,A Gowrisankar

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Fractal Patterns in Nonlinear Dynamics and Applications

By: Santo Banerjee,M K Hassan,Sayan Mukherjee,A Gowrisankar

Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.

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Page Count

207

Publisher

CRC Press

Published Date

ISBN 10

1498741363

ISBN 13

9781498741361

Book's by A. Gowrisankar

Fractal Functions, Dimensions and Signal Analysis

Fractal Functions, Dimensions and Signal Analysis

Fractal Patterns with MATLAB

Fractal Patterns with MATLAB

Fractal Patterns in Nonlinear Dynamics and Applications

Fractal Patterns in Nonlinear Dynamics and Applications

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