On the performance surfaces of a frequency domain adaptive IIR filter

The performance surface of a recently proposed frequency-domain adaptive IIR (infinite-impulse response) filter are analyzed. It is shown that for the sufficient-order case the surfaces are unimodal up to an equivalence class of N-factorial members where N is the number of adaptive poles. It is also shown that there exist manifolds separating the N-factorial members in the equivalence class from each other. On these manifolds lie saddle points. These saddle points cause slow convergence which appears to be shoulders on the MSE (mean-squared error) convergence curves. This can be avoided by initializing adaption away from the manifolds. Methods of finding saddle points are given. A second-order example confirms the above results