Synchronous adaptive filters with delayed coefficient adaption

The authors present exact descriptions of the behaviour of a class of adaptive filters with delayed coefficient adaption. This coefficient update delay is demonstrated to occur as a natural consequence of introducing compensation for nonminimum phase systems under the control of a least mean square based adaptive filter, as in the adaptive control of acoustic noise. A linear, time-invariant equivalent transfer function model of the adaptive system is developed, which can be used to study steady-state performance and the stability limits imposed by the coefficient update delay