This paper proposes a novel unconstrained monitoring system that measures heart and respiratory rates and evaluates autonomic nervous activity based on heart rate variability. The proposed system measures the aortic pulse waves (APWs) of a patient via an APW sensor that comprises a single microphone integrated into a mattress. Vital signs (i.e., heart rate, respiratory rate) and autonomic nervous activity were analyzed using the measured APWs. In an experiment with supine and seated participants, vital signs calculated by the proposed system were compared with vital signs measured with commercial devices, and we obtained the correlations of r > 0.8 for the heart rates, r > 0.7 for the respiratory rates, and r > 0.8 for the heart rate variability indices. These results indicate that the proposed system can produce accurate vital sign measurements. In addition, we performed the experiment of image stimulus presentation and explored the relationships between the self-reported psychological states evoked by the stimulus and the measured vital signs. The results indicated that vital signs reflect psychological states. In conclusion, the proposed system demonstrated its ability to monitor health conditions by actions as simple as sitting or lying on the APW sensor.