Constant-Order Fractional Signal Processing

Part of the Signals and Communication Technology book series (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.

Keywords

Autocorrelation Bide 

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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.School of Electronic and Information EngineeringDalian Jiaotong UniversityDalianPeople’s Republic of China
  2. 2.Department of Electrical and Computer Engineering, CSOISUtah State UniversityLoganUSA
  3. 3.School of Electronic and Information EngineeringDalian University of TechnologyDalianPeople’s Republic of China

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