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A detection system usually contains a predetection filter whose function is to enhance the strength of the signal relative to that of the noise. An optimum predetection filter is defined in this paper as one which maximizes the "distance" between the signal and noise components of the output (subject to a constraint on the noise compgnent) in terms of a suitable distance function d(x, y). In a special case, this definition leads to the criterion used by North, and yields filters which maximize the signal-to-noise ratio at a specified instant of time. North's theory of such filters is extended to the case of nonwhite noise and finite memory (i.e., finite observation time) filters. Explicit expressions for the impulsive responses of such filters are developed, and two examples of practical interest are considered.