Scaling Fractals and Wavelets

Scaling  Fractals and Wavelets
Author: Patrice Abry,Paolo Goncalves,Jacques Levy Vehel
Publsiher: John Wiley & Sons
Total Pages: 382
Release: 2013-03-01
Genre: Mathematics
ISBN: 9781118622902

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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.

Wavelets and Fractals in Earth System Sciences

Wavelets and Fractals in Earth System Sciences
Author: E. Chandrasekhar,V. P. Dimri,V. M. Gadre
Publsiher: Taylor & Francis
Total Pages: 306
Release: 2013-11-20
Genre: Science
ISBN: 9781466553606

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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 w

Wavelets Vibrations and Scalings

Wavelets  Vibrations  and Scalings
Author: Yves Meyer
Publsiher: Unknown
Total Pages: 133
Release: 1997
Genre: Fractals
ISBN: 1470438550

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Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area. There is a widely accepted belief that wavelet analysis should provide the best available tool to unveil such scaling laws. And orthonormal wavelet bases are the only existing bases which are structurally invariant through dyadic dilati.

Signal Processing with Fractals

Signal Processing with Fractals
Author: Gregory W. Wornell,Gregory Wornell
Publsiher: Prentice Hall
Total Pages: 200
Release: 1996
Genre: Mathematics
ISBN: UOM:39015034528383

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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.

Wavelets Fractals and Fourier Transforms

Wavelets  Fractals  and Fourier Transforms
Author: M. Farge,Julian C. R. Hunt,J. C. Vassilicos
Publsiher: Unknown
Total Pages: 432
Release: 1993
Genre: Mathematics
ISBN: UOM:39015029896126

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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

Analysis and Probability

Analysis and Probability
Author: Palle E. T. Jorgensen
Publsiher: Springer Science & Business Media
Total Pages: 320
Release: 2007-10-17
Genre: Mathematics
ISBN: 9780387330822

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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

Wavelets and Wavelet Transform Systems and Their Applications

Wavelets and Wavelet Transform Systems and Their Applications
Author: Cajetan M. Akujuobi
Publsiher: Springer Nature
Total Pages: 657
Release: 2022-02-02
Genre: Technology & Engineering
ISBN: 9783030875282

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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.

Wavelets and Fractals in Earth System Sciences

Wavelets and Fractals in Earth System Sciences
Author: E. Chandrasekhar,V. P. Dimri,V. M. Gadre
Publsiher: Taylor & Francis
Total Pages: 308
Release: 2013-11-20
Genre: Science
ISBN: 9781466553590

Download Wavelets and Fractals in Earth System Sciences Book in PDF, Epub and Kindle

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.