On new classes of matched filters and generalizations of the matched filter concept
David Middleton · IEEE Transactions on Information Theory · 1960
In this paper it is shown how the earlier concepts of the matched filter may be generalized by recognizing explicitly the decision-making character of most reception systems. Accordingly, when an approach making use of statistical decision theory is applied for both signal detection and extraction, a variety of new classes of matched filters (Bayes matched filters) can be defined. These can be described specifically in the critical situation of threshold reception, where system optimality is at a premium. It is shown, for incoherent reception in some important special instances, that matched filters based on maximizing output signal-to-noise ratio (theS/Nmatched filters of the earlier theory) are also optimum from the broader, decision viewpoint. The required optimum filters are themselves time-varying and nonunique, and thus permit a measure of design freedom. In all instances, realizable filters are possible, and it is shown how their weighting functions may be determined. Both discrete and continuous filtering on a finite interval,(0, T), are considered.