Rational Variable Projection Methods in ECG Signal Processing
In this paper we develop an adaptive electrocardiogram (ECG) model based on rational functions. We approximate the original signal by the partial sums of the corresponding Malmquist–Takenaka–Fourier series. Our aim in the construction of the model was twofold. Namely, besides good approximation an equally important point was to have direct connection with medical features. To this order, we consider the rational optimization problem as a special variable projection method. Based on the natural segmentation of a heartbeat into P, QRS, T waves, we use three complex parameters, i.e. the poles of the rational functions. For the optimization of the parameters, we apply constrained optimization. As a result every pole corresponds to one of these waves. We developed and tested our method by using the MIT-BIH Arrhythmia Database.
KeywordsMalmquist–Takenaka system Constrained optimization ECG modeling
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