On new classes of matched filters and generalizations of the matched filter concept

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 (the matched 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, , are considered.