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Fractional Calculus and Applied Analysis

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Impulse response of a generalized fractional second order filter

Zhuang Jiao
  • Department of Automation, Tsinghua University, Beijing, 100084, P.R. China
  • Center for Self-Organizing and Intelligent Systems (CSOIS), Electrical and Computer Engineering Department, Utah State University, Logan, UT, 84322, USA
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/ YangQuan Chen
  • Center for Self-Organizing and Intelligent Systems (CSOIS), Electrical and Computer Engineering Department, Utah State University, Logan, UT, 84322, USA
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Published Online: 2011-12-29 | DOI: https://doi.org/10.2478/s13540-012-0007-2

Abstract

The impulse response of a generalized fractional second order filter of the form (s 2α + as α + b)−γ is derived, where 0 < α ≤ 1, 0 < γ < 2. The asymptotic properties of the impulse responses are obtained for two cases, and within these two cases, the properties are shown when changing the value of γ. It is shown that only when (s 2α + as α + b)−1 has the critical stability property, the generalized fractional second order filter (s 2α + as α + b)−γ has different properties as we change the value of γ. Finally, numerical examples to illustrate the impulse response are provided to verify the obtained results.

MSC: Primary 26A33; Secondary 33E12, 34A08, 34K37, 35R11, 60G22

Keywords: generalized fractional second order filter; fractional-order signal processing; impulse response; critically stable

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About the article

Published Online: 2011-12-29

Published in Print: 2012-03-01


Citation Information: Fractional Calculus and Applied Analysis, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-012-0007-2.

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