Impulse response invariant discretization of a generalized commensurate fractional order filter

In this paper, we derive the impulse response of a generalized commensurate fractional-order filter of the form (s^2α+as^α+b)^-γ, where a, b ≥ 0, α ∈ (0, 1] and γ ∈ (0, 1). 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-order filter. Finally, a number of illustrated examples in time and frequency domains are provided as proofs of concepts.