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Threshold coherent and incoherent detection of signals in normal noise is examined when random data sampling is employed at the receiver. The resulting optimum system and its threshold performance are compared with the corresponding cases where periodic sampling is used. Expressions for the system structure, the error probabilities, and the Bayes risk are obtained; for the specific examples examined it is found that periodic sampling gives better performance than random sampling. A discussion of the generality of these results is given in the concluding section.