Filter design involves a trade-off between the size of the filter class over which optimization is to be performed and the size of the training sample. As the number of parameters determining the filter class grows, so too does the size of the training sample required to obtain a given degree of precision when estimating the optimal filter from the sample data. The present paper considers an approach that allows a larger number of observations to be taken into account by constraining optimization of a binary filter to a function class that includes the fully optimal mean-absolute-error filter over a given subwindow. It does so by dividing the observation window into primary and secondary windows, and by defining a class of Boolean functions that includes all filters over the primary window. This means that optimization is unconstrained relative to the variables in the primary window and constrained relative to the variables in the secondary window. Filter representation, error expression, and design methodology relative to the window decomposition are discussed. Special attention is paid to the constraint of linearly separability in the secondary window. In particular, a new iterative algorithm for estimating optimal linearly separable functions from their error surface is proposed. 1998 Elsevier Science B.V. All rights reserved.
