For optimal sensory processing, neural circuits must extract novel, unpredictable signals from the redundant sensory input in which they are embedded, but the detailed cellular and network mechanisms that implement such selective cancellation are presently unknown. Using a combination of modeling and experiment, we characterize in detail a cerebellar circuit in weakly electric fish, showing how it can carry out this computation. We use a model incorporating the wide range of experimentally estimated parallel fiber feedback delays and a burst-induced LTD rule derived from in vitro experiments to explain the precise cancellation of redundant signals observed in vivo. Our model demonstrates how the backpropagation-dependent burst dynamics adjusts the temporal pairing width of the plasticity mechanism to precisely match the frequency of the redundant signal. The model also makes the prediction that this cerebellar feedback pathway must be composed of frequency-tuned channels; this prediction is subsequently verified in vivo, highlighting a novel and general capability of cerebellar circuitry.