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Objective. For the first time in the literature, this paper investigates some crucial aspects of blood pressure (BP) monitoring using photoplethysmogram (PPG) and electrocardiogram (ECG). In general, the proposed approaches utilize two types of features: parameters extracted from physiological models or machine-learned features. To provide an overview of the different feature extraction methods, we assess the performance of these features and their combinations. We also explore the importance of the ECG waveform. Although ECG contains critical information, most models merely use it as a time reference. To take this one step further, we investigate the effect of its waveform on the performance. Approach. We extracted 27 commonly used physiological parameters in the literature. In addition, convolutional neural networks (CNNs) were deployed to define deep-learned representations. We applied the CNNs to extract two different feature sets from the PPG segments alone and alongside corresponding ECG segments. Then, the extracted feature vectors and their combinations were fed into various regression models to evaluate our hypotheses. Main results. We performed our evaluations using data collected from 200 subjects. The results were analyzed by the mean difference t-test and graphical methods. Our results confirm that the ECG waveform contains important information and helps us to improve accuracy. The comparison of the physiological parameters and machine-learned features also reveals the superiority of machine-learned representations. Moreover, our results highlight that the combination of these feature sets does not provide any additional information. Significance. We conclude that CNN feature extractors provide us with concise and precise representations of ECG and PPG for BP monitoring. [ABSTRACT FROM AUTHOR]