1. An apparatus, comprising: a digital filter having a input for receiving tap values; and an optimization system for supplying tap values to the input of the digital filter, the optimization system including: a tap selector that establishes a search space of vectors, where a given vector represents a set of tap values for the digital filter at a first resolution, and selects a vector from the established search space; and a filter evaluator that evaluates the performance of the digital filter configured with the tap values represented by the selected vector and determines a performance metric for the selected vector, the tap selector being operative to select a best vector from the search space of vectors based upon the determined performance metrics for the search space of vectors and to generate a new search space of vectors, each of the vectors in the new search space representing a set of tap values at a second resolution that is higher than the first resolution.