The direct design of recursive or IIR digital filters

This paper introduces an Iterative Reweighted Least Squares method (IRLS) to design IIR filters that only requires magnitude specifications. While some common approaches for IIR design require the user to provide both magnitude and phase responses, doing so limits the optimality of a filter by forcing an algorithm to meet the specified phase. By allowing an algorithm to adjust the phase at each iteration in order to improve the magnitude one can expect better magnitude responses. The L
p
norm is used as a more general error measure than the commonly used L
2
and L
∞
norms. In this paper we extend some previous ideas from L
p
FIR design together with a method suggested independently by Leland Jackson and Atmadji Soewito to achieve magnitude optimality. While robust and efficient, the proposed method is flexible enough to allow for a combination of norms in different bands, allowing solutions for a variety of problems.