Impulse response of a generalized fractional second order filter

Zhuang Jiao; YangQuan Chen

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arXiv · 1106.1220

Impulse response of a generalized fractional second order filter

Zhuang Jiao·YangQuan Chen

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Abstract

The impulse response of a generalized fractional second order filter of the form ${{({{s}^{2\alpha}}+a{{s}^{\alpha}}+b)}^{-\gamma}}$ is derived, where $0<\alpha \le 1$, $0<\gamma <2$. The asymptotic properties of the impulse responses are obtained for two cases, and the two cases show the similar properties for the changing of $\gamma$ values. It is shown that only when ${{({{s}^{2\alpha}}+a{{s}^{\alpha}}+b)}^{-1}}$ has the critical stability, the generalized fractional second order filter ${{({{s}^{2\alpha}}+a{{s}^{\alpha}}+b)}^{-\gamma}}$ has different properties as we change the value of $\gamma$. Finally, numerical examples to illustrate the impulse response are provided to verify the proposed concepts.

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BibTeX RIS

Zhuang Jiao, YangQuan Chen. 2011-06-07. Impulse response of a generalized fractional second order filter. https://arxiv.org/abs/1106.1220

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