In several recent papers we have described a new kind of signal processing pattern recognition filter designed to be used exactly as matched filters are presently used. The new filter is usually superior to the matched filter in terms of both between-class discrimination and within-class tolerance. Because it has these properties and reduces to the matched filter for simple enough cases, the new filter is called the generalized matched filter (GMF). In this paper we give further detail on GMF derivation and operation. Particular stress is laid on the effects of the difference in optimization criteria for those simple cases for which both the matched filter and the GMF are defined.