Normalization and convergence of adaptive IIR filters

Several algorithms for adaptive IIR (infinite impulse response) filters have been proposed. However, their practical use involves considerations such as finding the global minimum, the possible occurrence of instability, and uncertainty about the speed of convergence. A generalization of these adaptive IIR algorithms is presented here. The algorithms can be classified into two groups: those which do not filter the adaptation error and those which do. For the first group a normalization is presented and convergence is proven. For the second group, ideas for normalizations are presented and conditions for convergence are given. Special constraints for normalizations are also considered.<>