A polyphase IIR adaptive filter: error surface analysis and application

An analysis of the local convergence speed of constant gain algorithms for direct form IIR adaptive ̄lters is initially presented, showing the adverse e®ects that result from the proximity of the poles of the modelled system to the unit circle and, for complex poles, to the real axis. A global analysis of the reduced error surface in these cases is also presented, which shows that, away from the global minimum, there will be regions with an almost constant error, where the convergence of constant gain algorithms tends to be slow. A polyphase IIR adaptive ̄lter is then proposed and its local and global convergence properties are investigated, showing it to be specially well suited for applications with underdamped low-frequency poles. The polyphase structure is tested with di®erent constant gain algorithms in an echo-cancellation example, attaining a gain of 14 to 70 times in global convergence speed over the direct form, at the price of a relatively modest increase in computational complexity. A theorem concerning the existence of stationary points for the polyphase structure is also presented.