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An Overview of Fractional Processes and Fractional-Order Signal Processing Techniques

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Fractional Processes and Fractional-Order Signal Processing

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

Abstract

Chapter 2 provides an overview of basic concepts of fractional processes and fractional-order signal processing techniques from the perspective of fractional signals and fractional-order systems. Based on the fractional calculus, fractional-order systems are classified into three categories: constant-order fractional systems, variable-order fractional systems, and distributed-order fractional systems. Fractional processes, which can be considered as outputs of the fractional-order systems, have significant and complex long-memory properties. In order to best understand the fractional-order systems and extract valuable information from the fractional-order signals, fractional-order signal processing techniques are put forward for different kinds of fractional signals. All discussions on fractional-order signal processing techniques are centered around fractional calculus, fractional Fourier transform and α-stable distribution.

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Dalian Jiaotong University, Dalian, People’s Republic of China

    Hu Sheng

  2. Department of Electrical and Computer Engineering, CSOIS, Utah State University, Old Main Hill 4160, Logan, UT, 84322-4120, USA

    YangQuan Chen

  3. School of Electronic and Information Engineering, Dalian University of Technology, Dalian, People’s Republic of China

    TianShuang Qiu

Authors
  1. Hu Sheng
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  2. YangQuan Chen
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  3. TianShuang Qiu
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Correspondence to Hu Sheng .

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© 2012 Springer-Verlag London Limited

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Sheng, H., Chen, Y., Qiu, T. (2012). An Overview of Fractional Processes and Fractional-Order Signal Processing Techniques. In: Fractional Processes and Fractional-Order Signal Processing. Signals and Communication Technology. Springer, London. https://doi.org/10.1007/978-1-4471-2233-3_2

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  • DOI: https://doi.org/10.1007/978-1-4471-2233-3_2

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2232-6

  • Online ISBN: 978-1-4471-2233-3

  • eBook Packages: EngineeringEngineering (R0)

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