Equivalent transfer functions of minimum output variance mean-square estimators

An analysis of the behavior of adaptive filters designed around practically useful, minimum effort cost functions is presented. It is shown that equivalent transfer functions can be derived for both a conventional minimum variance system and for an estimator whose controlling algorithm attempts to minimize the norm square of the filter´s weight vector, this latter system being exactly equivalent to the leaky LMS (least mean squares) algorithm. Although the equivalent transfer functions are generally time variant, they assume time invariant form for several important classes of reference signal. In such cases the equivalent transfer function can be used to predict both transient and steady state aspects of the adaptive estimator´s performance, as demonstrated for the particularly important case of synchronous periodic estimation