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We consider the problem of blind estimation of a communication channel based on the oversampled channel output. We propose a nonparametric approach that, based on the cyclic spectrum of the output, finds the channel phase response without neither the need of phase unwrapping nor channel length information. For band-limited channels, the cyclic spectrum has limited support. For this case, we propose an approximation for the discretized phase of the cyclic spectrum that, under certain conditions, results in a simpler channel estimation method. The proposed approach is applied to simulated data and real recordings and is compared to existing methods.