Sleep Apnea Syndrome (SAS) is a prevalent but underdiagnosed condition associated with serious cardiovascular and cognitive consequences. Polysomnography (PSG), the diagnostic gold standard, is complex and costly, limiting its availability for home-based monitoring. In this study, we propose a method for automatic apnea detection using electroencephalogram (EEG) signals and Convolutional Neural Networks (CNNs), aiming to develop a less intrusive and more accessible diagnostic alternative. We trained and evaluated a CNN architecture using EEG recordings from the HomePAP dataset, applying both strict and non-strict segmentation strategies. A comprehensive hyperparameter optimization process was conducted, and performance was assessed through repeated ten-fold cross-validation using several evaluation metrics, including Area Under the Receiver Operating Characteristic (ROC) Curve (AUC), balanced F-score (F1-score), and Matthews Correlation Coefficient (MCC). The results show that the strict segmentation approach consistently outperformed the non-strict method, and that combining EEG with peripheral oxygen saturation (SaO₂) further improved classification accuracy. The best EEG-only configuration achieved an AUC of 0.689 under strict segmentation. Although showing modest performance, our findings support the possibility of detecting sleep apnea events through EEG signals and CNNs, particularly when designed for at-home monitoring scenarios, but additional research is necessary. Future work will need to explore improved segmentation strategies, model interpretability techniques and the incorporation of sleep stage information to enhance detection performance.