Generalized feed-forward filters: some theoretical results

The author presents theoretical results concerning a generalization of the transversal filter, called the generalized feedforward filter, where the unit delay of the tapped delay line is replaced by a general transfer function. A novel method of computing the partial derivatives of a performance function with respect to the tap-to-tap transfer function parameters in generalized feedforward filters is presented. Its application to the gamma filter results in an analytic method of computing the best value of mu (a parameter that controls the memory depth of the filter) and in an explanation of the peculiar structure of the squared error performance function. The theoretical results are illustrated by an example.<>