Abstract Objective. Sleep apnea is a common sleep breathing disorder that can significantly decrease sleep quality and have major health consequences. It is diagnosed based on the apnea hypopnea index (AHI). This study explored a novel, generalized algorithm for the automatic diagnosis of sleep apnea employing airflow (AF) and oximetry (SpO₂) signals. Approach. Of the 988 polysomnography records, 45 were randomly selected for developing the automatic algorithm and the remainder 943 for validating purposes. The algorithm detects apnea events by a per-sample encoding process applied to the peak excursion of AF signal. Hypopnea events were detected from the per-sample encoding of AF and SpO₂ with an adjustment to time lag in SpO₂. Total recording time was automatically processed and optimized for computation of total sleep time (TST). Total number of detected events and computed TST were used to estimate AHI. The estimated AHI was validated against the scored data from the Sleep Heart Health Study. Main results. Intraclass correlation coefficient of 0.94 was obtained between estimated and scored AHIs. The diagnostic accuracies were 93.5%, 92.4%, and 96.6% for AHI cut-off values of ≥5, ≥15, and ≥30 respectively. The overall accuracy for the combined severity categories (normal, mild, moderate, and severe) and kappa were 83.4% and 0.77 respectively. Significance. This new automatic technique was found to be superior to the other existing methods and can be applied to any portable sleep devices especially for home sleep apnea tests.