Routine ICU data offers valuable insights into daily physiological rhythms. While traditional methods assume these cycles maintain fixed periods and amplitudes, their inherent variability requires dynamic estimation of instantaneous trends. Wavelet transform effectively resolves circadian oscillations, especially for frequently measured vital parameters. We present novel extensions to the Continuous Wavelet Transform (CWT) power spectral analysis to better detect and segment subtle temporal patterns. Using this approach, we uncover hidden circadian patterns in cardiovascular vitals such as Heart Rate (HR) and Mean Blood Pressure (MBP) measured over five days in a retrospective cohort of 855 ICU patients. By quantifying non-stationary rhythms, we identified diurnal and semi-diurnal oscillations varying in period and power according to delirium and deep sedation. Notably, HR exhibits a clear diurnal and semi-diurnal rhythm when delirium is absent. Overall, our framework supports the CWT as a powerful tool for analyzing complex physiological signals, particularly vital signs. Crucially, our findings suggest that cardiovascular rhythm disruption can be associated with ICU-related delirium and deep sedation.