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.