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We present a biologically plausible mechanism to cancel simple redundant signals, i.e. sinusoidal waves, in neural circuits. Our mechanism involves the presence of: 1) stimulus-driven feedback to the neurons acting as detectors, 2) a large variety of temporal delays in the pathways transmitting such feedback, and 3) burst-induced long-term plasticity, all these factors being present in a wide set of neural systems. As an example, we consider the electrosensory lateral-line lobe of the weakly electric fish, which has been recently reported to employ this mechanism for the cancellation of redundant information in vivo. The cancellation is shown to be maintained for signals with different strengths of amplitude modulations.