Sleep staging is essential for evaluating sleep and its disorders. Most sleep studies today incorporate contact sensors that may interfere with natural sleep and may bias results. Moreover, the availability of sleep studies is limited, and many people with sleep disorders remain undiagnosed. Here, we present a pioneering approach for rapid eye movement (REM), non-REM, and wake staging (macro-sleep stages, MSS) estimation based on sleep sounds analysis. Our working hypothesis is that the properties of sleep sounds, such as breathing and movement, within each MSS are different. We recorded audio signals, using non-contact microphones, of 250 patients referred to a polysomnography (PSG) study in a sleep laboratory. We trained an ensemble of one-layer, feedforward neural network classifiers fed by time-series of sleep sounds to produce real-time and offline analyses. The audio-based system was validated and produced an epoch-by-epoch (standard 30-sec segments) agreement with PSG of 87% with Cohen's kappa of 0.7. This study shows the potential of audio signal analysis as a simple, convenient, and reliable MSS estimation without contact sensors.