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This paper develops the mathematical framework to analyze the stochastic resonance (SR) effect in binary hypothesis testing problems. The mechanism for SR noise enhanced signal detection is explored. The detection performance of a noise modified detector is derived in terms of the probability of detection PD and the probability of false alarm PFA. Furthermore, sufficient conditions are established to determine the improvability of a fixed detector using SR. The form of the optimal noise pdf is determined and the optimal stochastic resonance noise pdf which renders the maximum PD without increasing PFA is derived. Finally, an illustrative example is presented where performance comparisons are made between detectors where the optimal stochastic resonance noise, as well as Gaussian, uniform, and optimal symmetric noises are applied to enhance detection performance.