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Obstructive sleep apnea (OSA) is a common sleep disorder that causes pauses of breathing due to repetitive obstruction of the upper airways of the respiratory system. The effect of this phenomenon can be observed in other physiological signals like the heart rate variability, oxygen saturation, and the respiratory effort signals. In this study, features from these signals were extracted from 50 control and 50 OSA patients from the Sleep Heart Health Study database and implemented for minute and subject classifications. A support vector machine (SVM) classifier was used with linear and second-order polynomial kernels. For the minute classification, the respiratory features had the highest sensitivity while the oxygen saturation gave the highest specificity. The polynomial kernel always had better performance and the highest accuracy of 82.4% (Sen: 69.9%, Spec: 91.4%) was achieved using the combined-feature classifier. For subject classification, the polynomial kernel had a clear improvement in the oxygen saturation accuracy as the highest accuracy of 95% was achieved by both the oxygen saturation (Sen: 100%, Spec: 90.2%) and the combined-feature (Sen: 91.8%, Spec: 98.0%). Further analysis of the SVM with other kernel types might be useful for optimizing the classifier with the appropriate features for an OSA automated detection algorithm.