The impulse response of a generalized fractional second order filter of the form (s2α + asα + b)γ is derived, where 0 < α ≤ 1, γ > 0. The asymptotic properties of the impulse responses are obtained for two cases, and similar properties are shown for these two cases when we change the value of γ. It is shown that only when (s2α + asα + b)−1 has the critical stability, the generalized fractional second order filter (s2α + asα + 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 proposed concepts.

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