Iterative Design of lp FIR and IIR Digital Filters

This paper presents a family of algorithms to design FIR and IIR digital filters using l_p norms as optimality criteria. The algorithms presented are based on the iterative reweighted least squares (IRLS) method, and enjoy the same flexibility that traditional IRLS methods have. While other FIR methods use l₂ or l_iquest norms as design criteria, one can design filters that optimally compromise between these two criteria by using general l_p norms. Several important design problems can be solved by posing them as l_p problems (including the constrained least squares and magnitude l_p problems). This paper also presents IRLS algorithms to design complex l_p and magnitude l_p IIR filters. It is worth noting that the methods presented are based on a common theory, with changes mostly on the design of associated weighting functions. The methods are flexible, robust and typically converge rapidly.