The paper proposes a discrete-time algorithm for the rejection of sinusoidal disturbances of unknown frequency. The algorithm is adapted from an existing continuous-time algorithm and the overall nonlinear system is analyzed using a linear approximation. The paper shows that the noise rejection properties may be predicted using an in-phase/quadrature decomposition of the noise similar to the one encountered in the theory of phase-locked loops. Estimates are obtained for the standard deviations of the plant output and of the adaptive parameters. Simulations validate the predictions of the analysis, despite the nonlinear nature of the adaptive system and the high level of noise applied.