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The practice of integrating periodic low-level signals with time in order to improve the SNR of a coherent signal in an ambient of incoherent noise is extremely useful and generally understood. In cases where the signal continues as long as the observer desires to integrate, the SNR can of course be improved by lengthening the integration period without limit. However, in the case of a radar system trying to detect a very rapidly-approaching target, it is obvious that one does not have an unlimited length of time to perform the signal integration and arrive at a decision. The authors have derived an expression which reveals what the optimum integration period is when the radius of the region to be protected, and the velocity of the approaching target, are known.