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The detection of stationary Gaussian signals in a background of stationary Gaussian noise by the analog multiplier correlator, the polarity coincidence correlator (PCC), and the sample polarity coincidence correlator (SPCC) is considered. It is assumed that signal and noise have identical normalized autocovariance functions, and they are not cross correlated with each other. The main contributions of this paper are the exact expressions for the output signal-to-noise ratio (SNR) for the correlators mentioned for all values of the input SNR. It is shown that there exists a critical value of the input SNR, such that, whenever this value is exceeded, the PCC output SNR exceeds that of the analog correlator. A sufficient condition for this gain in output SNR is obtained in terms of the input SNR. This result is illustrated for stationary Gauss-Markov processes.