On the practical realization of higher-order filters with fractional stepping

We propose the use of a compact integer-order transfer function approximation of the fractional-order Laplacian operator sαsα to realize fractional-step filters. Lowpass and bandpass filters of orders (n+α)(n+α) and 2(n+α)2(n+α), where n   is an integer and 0<α<10<α<1, can, respectively, be designed. A 5th-order lowpass filter with fractional steps from 0.1 to 0.9 (i.e. 5.1→5.95.1→5.9) is given as an example with its characteristics compared to 5th- and 6th-order Butterworth filters. Spice simulations and experimental results are shown.