Obstructive sleep apnoea (OSA) is a sleep disorder with long-term consequences. Long-term effects include sleep-related issues and cardiovascular diseases. OSA is often diagnosed with an overnight sleep test called a polysomnogram. Monitoring can be costly with long wait times for diagnosis. In this paper, a novel OSA screening framework and prototype phone application are introduced. A database of 856 patients that underwent at-home polygraphy was collected. Features were derived from audio, actigraphy, photoplethysmography (PPG), and demographics, and used as the inputs of a support vector machine (SVM) classifier. The SVM was trained on 735 patients and tested on 121 patients. Classification on the test set had an accuracy of up to 92.2% when classifying subjects as having moderate or severe OSA versus being healthy or a snorer based on the clinicians' diagnoses. The signal processing and machine learning algorithms were ported to Java and integrated into the phone application-SleepAp. SleepAp records the body position, audio, actigraphy and PPG signals, and implements the clinically validated STOP-BANG questionnaire. It derives features from the signals and classifies the user as having OSA or not using the SVM trained on the clinical database. The resulting software could provide a new, easy-to-use, low-cost, and widely available modality for OSA screening.