Towards the realization of fractional step filters

In this paper we propose a fractional lowpass transfer function of the order (n + α) where n is an integer and 0 < α < 1. We show how this filter can be designed using an integer-order transfer function approximation of the fractional-order Laplacian operator s^α. A 1^st order lowpass filter with fractional steps from 0.1 to 0.9, that is of order 1.1 to 1.9 is given as an example with its characteristics compared to 1^st and 2^nd order Butterworth filters. PSPICE simulations and experimental results of a prototype filter verify the operation of the fractional step filter.