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Fractional Processes and Fractional-Order Signal Processing

Techniques and Applications

  • Hu Sheng
  • YangQuan Chen
  • TianShuang Qiu

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

  • Hu Sheng
    • 1
  • YangQuan Chen
    • 2
  • TianShuang Qiu
    • 3
  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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-2233-3
  • Copyright Information Springer-Verlag London Limited 2012
  • Publisher Name Springer, London
  • eBook Packages Engineering
  • Print ISBN 978-1-4471-2232-6
  • Online ISBN 978-1-4471-2233-3
  • Series Print ISSN 1860-4862
  • Buy this book on publisher's site