Alternate realizations to adaptive IIR filters and properties of their performance surfaces

It is shown how different structures of an adaptive filter lead to a change in the characteristics of the corresponding error surface and, consequently, to a change in the corresponding convergence rate and minimum mean-square error. Alternate realizations of adaptive infinite impulse response (IIR) filters are presented, and some properties of their performance surfaces are found through mathematical analysis. A parallel-form realization of adaptive IIR filters is introduced, and the behaviors of the recursive least-mean-square algorithm for this structure and for the direct form realization are compared. A general theory based on an analysis of stationary points is presented. This general result is then specialized for parallel and cascade realizations