DOI
10.34229/KCA2522-9664.26.4.15
UDC 519.6:519.7
M.S. Yefremov
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
yefremov@knu.ua
A.V. Liashko
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
andrey_liashko@knu.ua
O.B. Stelia
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine, Oleg.Stelya@gmail.com
B.V. Batsak
National Scientific Center "M.D. Strazhesko Institute of Cardiology, Clinical
and Regenerative Medicine" of the National Academy of Medical Sciences
of Ukraine, Kyiv, Ukraine, dr.batsak@gmail.com
Iu.V. Krak
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine;
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences
of Ukraine, Kyiv, Ukraine, iurii.krak@knu.ua
ACCURATE DETECTION OF R-PEAK IN ELECTROCARDIOGRAMS:
PIECEWISE-POLYNOMIAL APPROXIMATION, NOISE REDUCTION,
FIRST DERIVATIVE ANALYSIS
Abstract. The paper is devoted to the development of computationally efficient information technology for the automatic detection
of R-peaks in electrocardiograms, focused on portable long-term monitoring systems.
Scientific novelty is the study proposes a piecewise polynomial approximation method based on second-order
Hermite polynomials to transform discrete data into a continuous analytical signal representation.
This approach ensures the continuity of both the approximating function and its first derivative (smoothness),
enabling analytical gradient calculation. This minimizes noise impact and provides precise R-peak localization despite baseline drift and motion artifacts.
The mathematical framework is integrated into a clinical decision support system using a microservice architecture (FastAPI, Docker)
and vector-based visualization (D3.js). Results of testing on the MIT-BIH Arrhythmia Database showed high efficiency,
with an average F-score exceeding 99.1% and some complex cases 100% accuracy was achieved. The technology’s low computational cost makes it suitable for real-time cardiac monitoring in embedded systems and IoT devices.
Keywords: electrocardiogram, R-peaks, piecewise polynomial approximation, Hermite polynomials, analytical differentiation, smoothing of a discrete signal, information technologies, decision support.
full text
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