Analysis of a frequency-domain adaptive IIR filter

Convergence of frequency-domain adaptive pole-zero IIR (infinite impulse response) filter is studied. The algorithm is shown to converge in probability to an associated ordinary differential equation (ODE) which in turn converges to a local minimum of its performance surface. An analysis of the performance surface shows that the algorithm converges to one of N-factorial members in an equivalence class of global minimum points, where N is the number of adaptive poles. Saddle points exist on manifolds that separate members in the equivalence class. This explains `shoulders' in the MSE convergence curves and also suggests one way of avoiding these shoulders which cause slow convergence. A second-order simulation example confirms the above results