Analogue electronic active filter implementation of an approximate state space realisation of a fractional-order system

The paper presents a procedure of approximate implementation of a given fractional-order system as an electronic analogue active filter. Employment of LIRA method of impulse response approximation allows the filter to be only composed of standard RC components and operational amplifiers. A proposed state variable transformation helps to simplify filter structure and reduce component count while improving its noise properties and accuracy of integer-order prototype frequency response reproduction. The paper provides and compares results of realistic LTspice IV simulations for both implementations based on the LIRA realisation and its transfromed variant respectively. They confirm effectiveness of the presented approach involving LIRA approximation and state transformation steps.