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The purpose of this presentation is to develop and evaluate an algorithm for determining a finite memory detector applicable to statistical signal detection theory. In the Bayesian signal detection theory, infinite soft or changeable memory is tacitly assumed. Since an infinite memory is physically unrealizable, this study postulates a finite memory scheme which is applicable to a large class of signal detection problems. A general sequentially operating finite memory detector design is obtained and then evaluated for the signal known exactly and the signal known except amplitude problems. Detection performance as a function of memory size is presented for finite observation records using the receiver operating characteristic and plots of probability of decision error versus time. These results show the tradeoff between memory size and processing time to achieve a given detection performance. An important result is that for finite sample records a small finite memory detector with a memory size on the order of 7 states, i.e., a 3-bit computer word, yields detection performance very near that of the optimum infinite memory detector.