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Analytical impulse response of a fractional second order filter and its impulse response invariant discretization |
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| Authors: | Yan Li Hu Sheng YangQuan Chen |
| Affiliation: | a School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, PR China b Department of Electronic Engineering, Dalian University of Technology, Dalian 116024, PR China c Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical and Computer Engineering, Utah State University, 4120 Old Main Hill, Logan, UT 84322, USA |
| Abstract: | In this paper, we derive the impulse response of a fractional second order filter of the form (s2+as+b)−γ, where a,b?0 and γ>0. The asymptotic properties of the impulse responses are obtained. Moreover, based on the derived analytical impulse response, we show how to perform the discretization of the above fractional second order filter. Finally, a number of illustrated examples in time and frequency domains are provided as proofs of concepts. |
| Keywords: | Fractional order filter Complex integral Discretization method |
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