Fractional Processes and Fractional-Order Signal Processing, 2012
Techniques and Applications
Signals and Communication Technology Series

Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ?fractional? perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing:   presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems;   introduces FOSP techniques and the fractional signals and fractional systems point of view;   details real-world-application examples of FOSP techniques to demonstrate their utility; and   provides important background material on Mittag?Leffler functions, the use of numerical inverse Laplace transform algorithms and supporting MATLAB® codes together with a helpful survey of relevant webpages. Readers will be able to use the techniques presented to re-examine their signals and signal-processing methods. This text offers an extended toolbox for complex signals from diverse fields in science and engineering. It will give academic researchers and practitioners a novel insight into the complex random signals characterized by fractional properties, and some powerful tools to analyze those signals.

Part I: Overview of Fractional Processes and Fractional-order Signal Processing.- Introduction.- Overview of Fractional Processes and Fractional-order Signal Processing.- Part II: Fractional Processes.- Constant-order Fractional Processes.- Multifractional Processes.- Part III: Fractional-order Signal Processing.- Constant-order Fractional Signal Processing.- Variable-order Fractional Signal Processing.- Distributed-order Fractional Signal Processing.- Part IV: Applications of Fractional-order Signal Processing Techniques.- FARIMA with Stable Innovations Model of Great Salt Lake Elevation.- Analysis of ECN Using Fractional Signal Processing Techniques.- Optimal Fractional-order Damping Strategies.- Heavy-tailed Distribution and Local Long Memory in Molecular Motion.- Multifractional Property Analysis of Human Sleep EEG Signals.- Conclusions.- Appendices: Mittag-Leffler Functions; Application of Numerical Inverse Laplace Transform Algorithms in Fractional-order Signal Processing; Some Useful Webpages; MATLAB® Codes of Impulse–Response Invariant Discretization of Fractional-order Filters.

Doctor YangQuan Chen has authored over 200 academic papers plus numerous technical reports. He co-authored two textbooks: "System Simulation Techniques with MATLAB®/Simulink" (with Dingyu Xue . Tsinghua University Press, April 2002, ISBN 7-302-05341-3/TP3137, in Chinese) and "Solving Advanced Applied Mathematical Problems Using Matlab" (with Dingyu Xue. Tsinghua University Press. August 2004. 419 pages in Chinese, ISBN 7-302-09311-3/O.392); and six research monographs: "Plastic Belt for Projectiles" (with Y. Shi. Shaanxi Science and Technology Press, Jan. 1995, ISBN 7-5369-2277-9/TJ.1, in Chinese), "Iterative Learning Control " (with C. Wen . Lecture Notes in Control and Information Sciences, Springer-Verlag, Nov. 1999, ISBN: 978-1-85233-190-0), “Iterative Learning Control” (with Hyo-Sung Ahn and Kevin L. Moore. Springer, July 2007, ISBN: 978-1-84628-846-3), “Optimal Observation for Cyber-physical Systems”(with Zhen Song, Chellury Sastry and Nazif Tas. Springer, July 2009, ISBN: 978-1-84882-655-7), “Fractional-order Systems and Controls” (with Concepción A. Monje, Blas M. Vinagre, Dingyu Xue and Vicente Feliu, ISBN: 978-1-84996-334-3), and “Optimal Mobile Sensing and Actuation Strategies in Cyber-physical Systems” (with Christophe Tricaud). His current research interests include autonomous navigation and intelligent control of a team of unmanned ground vehicles, machine vision for control and automation, distributed control systems (MAS-net: mobile actuator-sensor networks), fractional-order control, interval computation, and iterative/repetitive/adaptive learning control. Currently, he serves as an Associate Editor for IEEE Control Systems Society, Conference Editorial Board (CSSCEB ). He was also an Associate Editor of ISA Review Board for AACC 's American Control Conference ( ACC2005 ). He has been the Co-Organizer and Instructor of the Tutorial Workshops on “Fractional-order Calculus in Control and Robotics” at IEEE 2002 Conference onDecision and Control (CDC’0

Clear introduction to the need for and existing tools of inquiry into the world of fractional-order signal processing Emphasizes a computational approach with MATLAB® codes provided Practical real-world applications in diverse fields are presented as examples of the usefulness of fractional-order signal-processing techniques Includes supplementary material: sn.pub/extras