Although sleep apnea is one of the most prevalent sleep disorders, most patients remain undiagnosed and untreated. The gold standard for sleep apnea diagnosis, polysomnography, has important limitations such as its high cost and complexity. This leads to a growing need for novel cost-effective systems. Mobile health tools and deep learning algorithms are nowadays being proposed as innovative solutions for automatic apnea detection. In this work, a convolutional neural network (CNN) is trained for the identification of apnea events from the spectrograms of audio signals recorded with a smartphone. A systematic comparison of the effect of different window sizes on the model performance is provided. According to the results, the best models are obtained with 60 s windows (sensitivity-0.72, specilicity-0.89, AUROC = 0.88), For smaller windows, the model performance can be negatively impacted, because the windows become shorter than most apnea events, by which sound reductions can no longer be appreciated. On the other hand, longer windows tend to include multiple or mixed events, that will confound the model. This careful trade-off demonstrates the importance of selecting a proper window size to obtain models with adequate predictive power. This paper shows that CNNs applied to smartphone audio signals can facilitate sleep apnea detection in a realistic setting and is a first step towards an automated method to assist sleep technicians. Clinical Relevance- The results show the effect of the window size on the predictive power of CNNs for apnea detection. Furthermore, the potential of smartphones, audio signals, and deep neural networks for automatic sleep apnea screening is demonstrated.