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This paper is concerned with the analysis of the performance of a zero-crossing type of frequency discriminator when the input signal is a narrow-band Gaussian random process. The sensitivity and the amount of ripple in the output voltage of such a discriminator are found in terms of the autocorrelation function of the input signal. The tracking error and the output frequency jitter of a closed-loop frequency tracker utilizing this discriminator are then found. The predicted jitter of the tracker frequency for this discriminator compares well with the theoretically achievable value found by previous authors. The analysis technique is sufficiently general so that it can be adapted to other types of zero-crossing discriminators.