Polysomnographic signals are usually recorded from patients exhibiting symptoms related to sleep disorders such as obstructive sleep apnea (OSA). Analysis of polysomnographic data allows for the determination of the type and severity of sleep apnea or other sleep-related disorders by a specialist or technician. The usual procedure entails an overnight recording several hours long. This paper presents a methodology to help with the screening of OSA using a 5-min oronasal airway pressure signal emanating from a polysomnographic recording during the awake period, eschewing the need for an overnight recording. The clinical sample consisted of a total of 41 subjects, 20 non-OSA individuals and 21 individuals with OSA. A signal analysis technique based on the Hilbert–Huang transform was used to extract intrinsic oscillatory modes from the signals. The frequency distribution of both the first mode and second mode and their sum were shown to differ significantly between non-OSA subjects and OSA patients. An index measure based on the distribution frequencies of the oscillatory modes yielded a sensitivity of 81.0% (for 95% specificity) for the detection of OSA. Two other index measures based on the relation between the area and the maximum of the 1st and 2nd halves of the frequency histogram both yielded a sensitivity of 76.2% (for 95% specificity). Although further tests will be needed to test the reproducibility of these results, the proposed measures seem to provide a fast method to screen OSA patients, thus reducing the costs and the waiting time for diagnosis.