Scaling, Fractals and Wavelets
Scaling, Fractals and Wavelets

Author: Patrice Abry

Publisher: John Wiley & Sons

Published: 2013-03-01

Total Pages: 382

ISBN-13: 1118622901

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Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.

Signal Processing with Fractals
Signal Processing with Fractals

Author: Gregory W. Wornell

Publisher: Prentice Hall

Published: 1996

Total Pages: 200

ISBN-13:

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Fractal geometry and recent developments in wavelet theory are having an important impact on the field of signal processing. Efficient representations for fractal signals based on wavelets are opening up new applications for signal processing, and providing better solutions to problems in existing applications. Signal Processing with Fractals provides a valuable introduction to this new and exciting area, and develops a powerful conceptual foundation for understanding the topic. Practical techniques for synthesizing, analyzing, and processing fractal signals for a wide range of applications are developed in detail, and novel applications in communications are explored.

Analysis and Probability
Analysis and Probability

Author: Palle E. T. Jorgensen

Publisher: Springer Science & Business Media

Published: 2007-10-17

Total Pages: 320

ISBN-13: 0387330828

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Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature

Fractal and Wavelet Image Compression Techniques
Fractal and Wavelet Image Compression Techniques

Author: Stephen T. Welstead

Publisher: SPIE Press

Published: 1999

Total Pages: 264

ISBN-13: 9780819435033

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Interest in image compression for internet and other multimedia applications has spurred research into compression techniques that will increase storage capabilities and transmission speed. This tutorial provides a practical guide to fractal and wavelet approaches--two techniques with exciting potential. It is intended for scientists, engineers, researchers, and students. It provides both introductory information and implementation details. Three Windows-compatible software systems are included so that readers can explore the new technologies in depth. Complete C/C++ source code is provided, enabling readers to go beyond the accompanying software. The mathematical presentation is accessible to advanced undergraduate or beginning graduate students in technical fields.

Wavelets and Fractals in Earth System Sciences
Wavelets and Fractals in Earth System Sciences

Author: E. Chandrasekhar

Publisher: Taylor & Francis

Published: 2013-11-20

Total Pages: 308

ISBN-13: 1466553596

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The subject of wavelet analysis and fractal analysis is fast developing and has drawn a great deal of attention in varied disciplines of science and engineering. Over the past couple of decades, wavelets, multiresolution, and multifractal analyses have been formalized into a thorough mathematical framework and have found a variety of applications with significant impact in several branches of earth system sciences. Wavelets and Fractals in Earth System Sciences highlights the role of advanced data processing techniques in present-day research in various fields of earth system sciences. The book consists of ten chapters, providing a well-balanced blend of information about the role of wavelets, fractals, and multifractal analyses with the latest examples of their application in various research fields. By combining basics with advanced material, this book introduces concepts as needed and serves as an excellent introductory material and also as an advanced reference text for students and researchers.

Wavelet Radio
Wavelet Radio

Author: Homayoun Nikookar

Publisher: Cambridge University Press

Published: 2013-03-21

Total Pages: 211

ISBN-13: 110731092X

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The first book to provide a detailed discussion of the application of wavelets in wireless communications, this is an invaluable source of information for graduate students, researchers, and telecommunications engineers, managers and strategists. It overviews applications, explains how to design new wavelets and compares wavelet technology with existing OFDM technology. • Addresses the applications and challenges of wavelet technology for a range of wireless communication domains • Aids in the understanding of Wavelet Packet Modulation and compares it with OFDM • Includes tutorials on convex optimisation, spectral factorisation and the design of wavelets • Explains design methods for new wavelet technologies for wireless communications, addressing many challenges, such as peak-to-average power ratio reduction, interference mitigation, reduction of sensitivity to time, frequency and phase offsets, and efficient usage of wireless resources • Describes the application of wavelet radio in spectrum sensing of cognitive radio systems.

Fractal Functions, Fractal Surfaces, and Wavelets
Fractal Functions, Fractal Surfaces, and Wavelets

Author: Peter R. Massopust

Publisher: Academic Press

Published: 2016-09-02

Total Pages: 428

ISBN-13: 0128044705

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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

Wavelets, Fractals, and Fourier Transforms
Wavelets, Fractals, and Fourier Transforms

Author: M. Farge

Publisher:

Published: 1993

Total Pages: 432

ISBN-13:

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Proceedings of a conference in Cambridge, England, December 1990. Topics include wavelets, fractals, and order-two densities; iterated function systems and their applications; fractional Brownian motion and wavelets; wavelets and astronomical image analysis; the wavelet transform applied to flow around Antarctica; wavelet analysis of turbulence; solution of Burgers' equation by Fourier transform methods; the fractal dimension of oil-water interfaces in channel flows; and fractal aggregates in the atmosphere. No index. Annotation copyright by Book News, Inc., Portland, OR

Fractals, Wavelets, and their Applications
Fractals, Wavelets, and their Applications

Author: Christoph Bandt

Publisher: Springer

Published: 2014-09-27

Total Pages: 499

ISBN-13: 3319081055

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Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.

Wavelets and Wavelet Transform Systems and Their Applications
Wavelets and Wavelet Transform Systems and Their Applications

Author: Cajetan M. Akujuobi

Publisher: Springer Nature

Published: 2022-02-02

Total Pages: 657

ISBN-13: 3030875288

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This textbook is unique because of its in-depth treatment of the applications of wavelets and wavelet transforms to many areas, across many disciplines. The book is written to serve the needs of a one or two semester course at either the undergraduate or graduate level. The author uses a very simplified, accessible approach that de-emphasizes mathematical rigor. The presentation includes many diagrams to illustrate points being discussed and uses MATLAB for all of application code. The author reinforces concepts introduced in the book with easy to grasp review questions and problems, tailored to each specific chapter for better mastery of the subject matter. This book enables students to understand the fundamental concepts of wavelets and wavelet transforms, as well as how to use them for problem solutions in digital signal and image processing, mixed-signal testing, space applications, aerospace applications, biomedical, cyber security, homeland security and many other application areas.