Multifractal Processes: Theory and Applications of Complex Fractal Structures (Applied and Numerical Harmonic Analysis)

Multifractal processes are assuming an increasingly prominent role in many diverse technical fields such as physics, telecommunications, biology, mathematics, and engineering. In Multifractal Processes, the authors offer a comprehensive treatment of multifractal structures that is unique in its balance between theory and practical applications. While presenting the theoretical foundation of multifractals, this self-contained volume encourages the reader to explore the utility of multifractals for analyzing physical processes representative of these numerous fields. As a key strength of Multifractal Processes, the application topics that are presented provide a step-by-step roadmap for incorporating multifractal models within a signal processing framework. Fundamental mathematical concepts are clearly explained in an intuitively appealing manner by relying on physical insights and simple geometric models. Similarly, the reader is guided through the pitfalls associated with processing real data and offered robust approaches for extracting multifractal information from noisy data. This volume especially highlights how multifractal processes permeate the scientific community. The authors employ numerous examples gleaned from such fields as fluid dynamics, agent-based simulations, and communication networks to illustrate both the strengths and weaknesses of multifractal models. Along the way, analysis tools are developed to aid in the interpretation of results. Aimed for use by both first-year graduate students and the practical engineer, this text will appeal to any researcher desiring to learn the secrets of multifractal processes.