Deep networks usually require a massive amount of labeled data for their training. Yet, such data may include some mistakes in the labels. Interestingly, networks have been shown to be robust to such errors. This work uses spectral analysis of their learned mapping to provide an explanation for their robustness. In particular, we relate the smoothness regularization that usually exists in conventional training to the attenuation of high frequencies, which mainly characterize noise. By using a connection between the smoothness and the spectral norm of the network weights, we suggest that one may further improve robustness via spectral normalization. Empirical experiments validate our claims and show the advantage of this normalization for classification with label noise.