Pole-zero placement algorithm for the design of digital filters with fractional-order rolloff

Abstract

Digital and analog filters are often used in the modeling of real-world systems. Many practical systems are better modeled by filters with fractional order rolloff. Finite integer-order transfer functions cannot represent fractional-order systems exactly. They can, however, approximate fractional-order systems, with the approximation quality depending on the order of the transfer functions and the methods used to design them. Several analog design techniques have been developed to realize and improve such approximations. To date, digital design techniques have been largely restricted to discretizations of existing analog solutions. This paper presents a novel approach to designing digital lowpass filters with fractional-order rolloff directly in the discrete domain through pole-zero placement. Filters designed using the proposed iterative technique are stable, have precisely definable cutoff frequencies, and do not suffer from the variations that can arise from transforming an existing analog design. The proposed technique is shown to outperform certain existing analog and digital design methods, both subjectively and by objective measures. To complement the proposed approach, a parameter-estimation routine is also introduced to alleviate some of the associated computational burden by reducing its reliance on iterative methods.