Analysis of alternative realizations of adaptive IIR filters

A general theory, based on an analysis of stationary points, presented which shows that whenever a direct-form IIR (infinite-impulse-response) filter with unimodal MSE (mean-squared-error) surface is transformed into an alternate realization, the MSE surface associated with the new structure may have additional stationary points, which are either new equivalent minima (and hence indistinguishable at the filter ouput), or saddle points, which are unstable solutions in the parameter space. The general theory is specialized to parallel and cascade forms. It is also shown that, for both the parallel and cascade forms, a gradient algorithm will find a global minimum as long as there is some noise present to jitter the solution away from the reduced-order manifolds which may contain saddle points. Experimental examples were presented to illustrate that the predicted behavior is indeed observed in practice.