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Objective: A patient-independent approach for continuous estimation of vital signs using robust spectro-temporal features derived from only photoplethysmogram (PPG) signal. Methods: In the pre-processing stage, we remove baseline shifts and artifacts of the PPG signal using Incremental Merge Segmentation with adaptive thresholding. From the cleaned PPG, we extract multiple parameters independent of individual patient PPG morphology for both Respiration Rate (RR) and Blood Pressure (BP). In addition, we derived a set of novel spectral and statistical features strongly correlated to BP. We proposed robust correlation-based feature selection methods for accurate RR estimates. For fewer computations and accurate measurements of BP, the most significant features are selected using correlation and mutual information measures in the feature engineering part. Finally, RR and BP are estimated using breath counting and a neural network regression model, respectively. Results: The proposed approach outperforms the current state-of-the-art in both RR and BP. The RR algorithm results in mean absolute errors (median, 25th-75th percentiles) of 0.4 (0.1–0.7) for CapnoBase dataset and 0.5(0.3-2.8) for BIDMC dataset without discarding any data window. Similarly, BP approach has been validated on a large dataset derived from MIMIC-II ($\sim$1700 records) which has errors (mean absolute, standard deviation) of 5.0(6.3) and 3.0(4.0) for systolic and diastolic BP, respectively. The results meet the American Association for the Advancement of Medical Instrumentation (AAMI) and British Hypertension Society (BHS) Class A criteria. Conclusion: By using robust features and feature selection methods, we alleviated patient dependency to have reliable estimates of vitals.