Normalization and convergence of gradient-based algorithms for adaptive IIR filters

Abstract

In the last years several algorithms for adaptive IIR filters have been proposed. However, their practical usage involves considerations such as finding the global minimum, possible occurrence of instability and uncertainty about the speed of convergence. Following a deterministic approach this paper presents a generalization of these adaptive IIR algorithms. The algorithms can be classified into two groups: those which do not and those which do filter the adaptation error. For the first group a normalization rule is presented and convergence properties assuming slow time-variant filters are given. Stronger results for general time-variant filters could only be given for a small set of algorithms. For the second group ideas of normalizations are presented and their effects for convergence are shown. Validity is proven by applying these ideas to the simplified hyperstable adaptive recursive filter (SHARF) algorithm. Considerations about special constraints for normalizations close the paper.