Impulse response of a generalized fractional second order filter

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.