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In this study, we present detection algorithms of characteristic points of the QRS and T waves based on the continuous wavelet transform (CWT) with splines. This technique can handle any integer scale and the analysis is not restricted to scales that are powers of two, which allows to use a wide range of scales and to more efficiently reduce noise and artifacts. Evaluation of the QRS detection algorithm performance has been done in eight ECG data files of the MIT-BIH database, and the accuracy has been of 99.5%. Evaluation of the detection algorithms of the QRS wave onset and offsets of QRS and T waves has been done in the CSE multi-lead measurement database, and the measurements were within the tolerance limits for deviations with respect of the manual measurements determined by the CSE experts. Therefore, the proposed algorithms to detect characteristic points of the QRS and T waves based on this technique allow the evaluation of the CWT in more scales, are robust to noise and artifacts and have the accuracy of a human expert.