Analytical impulse response of a fractional second order filter and its impulse response invariant discretization

In this paper, we derive the impulse response of a fractional second order filter of the form (s2+as+b)−γ(s2+as+b)−γ, where a,b⩾0a,b⩾0 and γ>0γ>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.