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. >