On the fractional-order distributed parameter low-pass filter

In this paper, we derive the analytical impulse response of a fractional-order distributed parameter low-pass filter of the form ∫_a^b 1/Ts^α+1dT, where ≤ a ≤ b and α ∈ (0, 1). The asymptotic properties of the impulse responses are obtained. Moreover, based on the derived analytical impulse response, we present a technique to perform the discretization of the above fractional-order filter. Finally, a number of illustrated figures are presented to validate the concepts.