Continuous glucose monitoring (CGM) provides high-resolution metabolic time series that exhibit strong nonlinearity, non-stationarity, and multiscale temporal structure. Conventional CGM metrics summarize variability but fail to explicitly characterize the underlying physiological rhythms and long-term trends. We propose a physics-constrained signal decomposition framework for CGM analysis based on empirical mode decomposition and Hilbert transform principles. By estimating characteristic periods of intrinsic mode functions through Hilbert-based instantaneous frequency analysis, the method enables robust separation of ultradian components, circadian rhythms, and long-term residual behavior at the individual level. A stopping criterion grounded in physiologically meaningful time scales prevents overdecomposition and ensures interpretability. The framework is demonstrated on CGM recordings from patients with recent acute coronary syndromes, illustrating its ability to extract stable circadian profiles and subject-specific residual dynamics suitable for phenotyping and longitudinal modeling. The proposed methodology is general and can be applied to a wide range of biomedical time series where adaptive, physics-informed decomposition is required.