This paper explores the deployment of mm-wave Frequency Modulated Continuous Wave (FMCW) radar for vital sign detection across multiple scenarios. We focus on overcoming the limitations of traditional sensing methods by enhancing signal processing techniques to capture subtle physiological changes effectively. Our study introduces novel adaptations of the Prony and MUSIC algorithms tailored for real-time heart and respiration rate monitoring, significantly advancing the accuracy and reliability of non-contact vital sign monitoring using radar technologies. Notably, these algorithms demonstrate a robust ability to suppress noise and harmonic interference. For instance, the mean absolute errors (MAE) for MUSIC and Prony in heart rate detection are 1.8 and 0.81, respectively, while for respiration rate, the MAEs are 1.01 and 0.8, respectively. These results underscore the potential of FMCW radar as a reliable, non-invasive solution for continuous vital sign monitoring in healthcare settings, particularly in clinical and emergency scenarios where traditional contact-based monitoring is impractical.