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A discrete-time adaptive algorithm is proposed to reject periodic disturbances in the case where the frequencies are unknown and a reference sensor is not available. The stability of the algorithm is analyzed using averaging theory, and the design of the parameters is based on the linearized averaged system. While the algorithm is first designed for rejecting periodic disturbances with one sinusoidal component, it is also extended to deal with cases where the disturbance has multiple sinusoidal components. A frequency separation method is proposed to prevent the frequency estimates from converging to the same value. The effectiveness of the adaptive scheme is validated in simulations and in experiments on an active noise control testbed.