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The paper presents a novel method for Compressed Sensing (CS) based sampling scheme, which is suitable for implementation in a real-time data acquisition system, for the Internet-of-Medical-Things (IoMT) era. The method relies on exploiting CS theory for bioelectrical signals, and in particular, in this paper, the electrocardiographic (ECG) type of signals are considered. The novelty of the method consists of designing the sensing matrix considering the information that is related to the auto-correlation coefficients from the observed signal. Thus, the mathematical model for CS based acquisition of ECG signals and its feasibility for practical implementation for an IoMT based system is described. The results presented herein clearly demonstrates the robustness and usefulness of the proposed method.