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This paper describes the automatic extraction of the P, Q, R, S and T waves of electrocardiographic recordings (ECGs), through the combined use of a new machine-learning algorithm termed generalized orthogonal forward regression (GOFR) and of a specific parameterized function termed Gaussian mesa function (GMF). GOFR breaks up the heartbeat signal into Gaussian mesa functions, in such a way that each wave is modeled by a single GMF; the model thus generated is easily interpretable by the physician. GOFR is an essential ingredient in a global procedure that locates the R wave after some simple pre-processing, extracts the characteristic shape of each heart beat, assigns P, Q, R, S and T labels through automatic classification, discriminates normal beats (NB) from abnormal beats (AB), and extracts features for diagnosis. The efficiency of the detection of the QRS complex, and of the discrimination of NB from AB, is assessed on the MIT and AHA databases; the labeling of the P and T wave is validated on the QTDB database.