Sleep disorders are diagnosed in sleep laboratories by polysomnography, a multi-parameter examination that monitors biological signals during sleep. The subsequent evaluation of the obtained records is very time-consuming. The goal of this study was to create an automatic system for evaluation of the airflow and SpO${}_2$ channels of polysomnography records, through the use of machine learning techniques and a large database, for apnea and desaturation detection (which is unusual in other studies). To that end, a convolutional neural network (CNN) was designed using hyperparameter optimization. It was then trained and tested for apnea and desaturation. The proposed CNN was compared with the commonly used k-nearest neighbors (k-NN) method. The classifiers were designed based on nasal airflow and blood oxygen saturation signals. The final neural network accuracy for apnea detection reached 84%, and that for desaturation detection was 74%, while the k-NN classifier reached accuracies of 83% and 64% for apnea detection and desaturation detection, respectively.