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Constant-Order Fractional Signal Processing

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Fractional Processes and Fractional-Order Signal Processing

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

Abstract

Chapter 5 introduces the constant-order fractional signal processing techniques. The constant-order fractional signal processing techniques includes the simulation of constant-order fractional processes, constant-order fractional system modeling, fractional-order filter, and analogue realization of constant-order fractional systems. The relationship between constant-order fractional processes and constant-order fractional systems is investigated. Based on this relationship, the fractional Gaussian noise and fractional stable noise can both be simulated using the constant-order fractional integrator. In order to capture the long-range dependent property of the constant-order fractional processes, some constant-order fractional models, including FARIMA, FIGARCH and FARIMA with stable innovations were introduced. In addition, a fractional second-order filter G(s)=(s 2+as+b)−γ and its asymptotic properties were studied. At the end of the chapter, the analogue realization of the constant-order fractional integrator and differentiator was provided to meet the needs of practical applications.

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Notes

  1. 1.

    http://www.mathworks.com/matlabcentral/fileexchange/8312.

  2. 2.

    http://www.mathworks.com/matlabcentral/fileexchange/3673.

  3. 3.

    http://www.mathworks.com/matlabcentral/fileexchange/3514.

  4. 4.

    http://www.mathworks.com/matlabcentral/fileexchange/authors/9097.

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Author information

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

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  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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Sheng, H., Chen, Y., Qiu, T. (2012). Constant-Order Fractional Signal Processing. In: Fractional Processes and Fractional-Order Signal Processing. Signals and Communication Technology. Springer, London. https://doi.org/10.1007/978-1-4471-2233-3_5

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  • DOI: https://doi.org/10.1007/978-1-4471-2233-3_5

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2232-6

  • Online ISBN: 978-1-4471-2233-3

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