Convolutional neural networks (CNN) have demonstrated state-of-the-art classification results in image categorization, but have received comparatively little attention for classification of one-dimensional physiological signals. We design a deep CNN architecture for automated sleep stage classiffication of human sleep EEG and EOG signals. The CNN proposed in this paper amply outperforms recent work that uses a different CNN architecture over a single-EEG-channel version of the same dataset. We show that the performance gains achieved by our network rely mainly on network depth, and not on the use of several signal channels. Performance of our approach is on par with human expert inter-scorer agreement. By examining the internal activation levels of our CNN, we find that it spontaneously discovers signal features such as sleep spindles and slow waves that figure prominently in sleep stage categorization as performed by human experts.