Misadjustment expressions for infinite impulse response adaptive filters

Expressions are derived for the misadjustment in Infinite Impulse Response Adaptive filters. The decomposition method [1] for solving difference equations with randomly time-varying coefficients is thereby employed. Specifically, it is shown how higher order terms in the decomposition of the output correspond to the excess error caused by measurement noise in the coefficients. A simple example of an all-pole adaptive filter is included. It is shown that the misadjustment is largely dependent on the pole locations of the optimal filter.