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© 2012

Fractional Processes and Fractional-Order Signal Processing

Techniques and Applications

  • 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

Book

Part of the Signals and Communication Technology book series (SCT)

Table of contents

  1. Front Matter
    Pages I-XXVI
  2. Overview of Fractional Processes and Fractional-Order Signal Processing Techniques

    1. Front Matter
      Pages 1-1
    2. Hu Sheng, YangQuan Chen, TianShuang Qiu
      Pages 3-29
  3. Fractional Processes

    1. Front Matter
      Pages 47-47
    2. Hu Sheng, YangQuan Chen, TianShuang Qiu
      Pages 49-76
    3. Hu Sheng, YangQuan Chen, TianShuang Qiu
      Pages 77-92
  4. Fractional-Order Signal Processing

    1. Front Matter
      Pages 93-93
    2. Hu Sheng, YangQuan Chen, TianShuang Qiu
      Pages 95-148
    3. Hu Sheng, YangQuan Chen, TianShuang Qiu
      Pages 149-160
    4. Hu Sheng, YangQuan Chen, TianShuang Qiu
      Pages 161-176
  5. Applications of Fractional-Order Signal Processing Techniques

    1. Front Matter
      Pages 177-177
    2. Hu Sheng, YangQuan Chen, TianShuang Qiu
      Pages 203-215
    3. Hu Sheng, YangQuan Chen, TianShuang Qiu
      Pages 243-250
    4. Hu Sheng, YangQuan Chen, TianShuang Qiu
      Pages 251-252
  6. Back Matter
    Pages 253-295

About this book

Introduction

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.

Keywords

Fractional Fourier Transform Fractional-order Random Processes Fractional-order Signal Processing Long-range Dependence Nonstationary Stochastic Processes Stable Processes

Authors and affiliations

  1. 1.School of Electr. & Inform. EngineeringDalian University of TechnologyDalianChina, People's Republic
  2. 2.and Computer Engineering, CSOISUtah State University, Dept. of ElectricLoganUSA
  3. 3.School of Electr. & Inform. EngineeringDalian University of TechnologyDalianChina, People's Republic

About the authors

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 on Decision and Control (CDC’02), and “Applied Fractional Calculus in Controls and Signal Processing” at CDC’10 and a founding member of the ASME subcommittee on “Fractional Dynamics”.

Bibliographic information

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Reviews

From the reviews:

“The book presents the theory and applications of an interesting domain in the area of signal science and technology: fractional processes and fractional order signal processing. … The volume gives answers to several important questions related to fractional systems … . A collection of very useful MATLAB codes is gives together with a useful list of Web addresses. Finally, we think that the present volume will soon become a reference book in the area of fractional signal processing and systems.” (Dumitru Stanomir, Zentralblatt MATH, Vol. 1245, 2012)