Efficient ECG Modeling using Polynomial Functions

Jokic, S.; Delić, Vlado; Perić, Zoran; Krčo, Srđan; Sakač, Dejan

doi:10.5755/j01.eee.110.4.304

Cited by 25 publications

(13 citation statements)

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“…Polynomial functions can also be used in for some other purposes related to signal processing e.g. efficient ECG modelling [14] or some other computer science applications such as curve fitting [15].…”

Section: Discussionmentioning

confidence: 99%

Constructed Polynomial Windows with High Attenuation of Sidelobes

Okarma

2013

ElAEE

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In the paper the idea of the constructed polynomial windows is presented together with the obtained results of their optimization towards low level of the sidelobes. The main advantages of the polynomial windows are their low computational complexity and ability to change their frequency properties by some modifications of the polynomial coefficients in the time domain. Both of these merits are preserved in the constructed polynomial windows family discussed in the paper and the additional profit is the possibility of using two lower order polynomials with additional switching operation with similar sidelobes' attenuation as for higher order standard polynomial windows.

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Section: Discussionmentioning

confidence: 99%

Constructed Polynomial Windows with High Attenuation of Sidelobes

Okarma

2013

ElAEE

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“…The ECG signals can easily be described using three different approaches for any research such as: time domain, frequency domain, and frequency-time domain. The classic approach in electrocardiology is to use techniques for analyzing the time domain of the signal.As a rule, the ECG mathematical models are represented as a Fourier series [9], polynomial functions [10,11] or by derivatives [12].…”

Section: Analysis Of Literary Data and Problem Statementmentioning

confidence: 99%

Use of Triangular Models of Non-Stationary Processes in Modeling Variability of Heart Rhythm

Akhiiezer

Dunaievska

Shyshkin

et al. 2019

Innovative Technologies and Scientific Solutions for Industries

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The subject matter is a mathematical model describing the process of heart rhythm variability, which is based on the use of triangular models of non-stationary random processes in the Hilbert space. The goal of the research is to develop a mathematical model of nonstationary processes of cardiac activity based on a triangular model. This research was the basis for the development of a Matlab model that implements the proposed method for analyzing heart rate variability. Tasks are: to give a description of the variability heart rate as a non-stationary process in Hilbert space in terms of correlation functions; to research the possibility of constructing a correlation and spectral theory of a non-stationary process using triangular models; to synthesize the mathematical model of nonstationary process on the basis of correlation theory for solving mathematical processing and forecasting tasks on the basis of ECG data. Using the proposed mathematical method, we implemented the Matlab model of a heart signal generator, which allowed us to synthesize an ECG with different variability parameters in noisy conditions. Methods of mathematical statistics, simulation modeling, theory of random processes and control theory are used in this work. Results of this research are as follows: 1) It has been shown that the new approach to the description of the HRV as a random process in the application of the triangular model in the Hilbert space made it possible to obtain expressions for the correlation function. 2) The imitation simulation showed the sensitivity of the method within the 5% error rate under the conditions of different types of influence on HRV. The qualitative assessment of the possibilities of the proposed models to generate artificial ECG provided the possibility of visual analysis by the cardiologist of the identity of the interpretation of real ECG records. The identities of modeling results were checked on time samples of electrocardiographs of 7 patients from open PhysioNet cardiographic libraries on samples with the duration T = 10 s. 3) The standard low-frequency oscillations and "white noise" barrier are clearly differentiated on the applied correlation function by the distribution of spectral density power within the frequency range of 0,15-0,3 Hz. Conclusion. The simulation results confirmed the correctness of the theoretical conclusions about the possibility of using models based on the representation of non-stationary processes in a triangular Hilbert space.

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“…Отличительная особенность аппроксимации данных несимметричной гауссовой функцией (22) состоит в том, что для определения параметра  (1) на основе МНК используются значения…”

Section: метод анализа диагностических признаков экгunclassified

“…В работах [1][2][3] предложено аппроксимировать элементы ЭКГ полиномиальными функциями. Другие авторы рассматривают возможность описания ЭКГ сплайн-функциями [4] или функцией Безье [5].…”

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An Effective Method for Analysis of the Diagnostic Features Based on Noisy Electrocardiogram

Fainzilberg¹,

Matushevych²

2016

Upr. sist. maš.

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Эффективный метод анализа диагностических признаков по зашумленной электрокардиограмме Предложен метод анализа основных электрокардиографических признаков ЭКГ на основе построения конструктивного алгоритма описания циклов сигнала совокупностью несимметричных гауссовых функций. Разработан конструктивный алгоритм решения задачи аналитическим методом, основанный на модификации критерия оптимальности метода наименьших квадратов и введения ограничения на интервал аппроксимации элементов сигнала. Представлены результаты численных экспериментов на модельных и реальных данных, подтвердившие эффективность предложенного алгоритма. Ключевые слова: диагностический признак ЭКГ, гауссова функция, аппроксимация, критерий оптимальности Запропоновано метод аналізу основних електрокардіограмних ознак ЕКГ на основі побудови конструктивного алгоритму опису циклів сигналу сукупністю несиметричних гаусових функцій. Розроблено конструктивний алгоритм розв'язання задачі аналітичним методом, заснований на модифікації критерію оптимальності методу найменших квадратів і введення обмежень на інтервал апроксимації елементів сигналу. Представлено результати чисельних експериментів на модельних та реальних даних, котрі підтвердили ефективність запропонованого алгоритму. Ключові слова: діагностична ознака ЕКГ, гаусова функція, апроксимація, критерій оптимальності.

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Efficient ECG Modeling using Polynomial Functions

Cited by 25 publications

References 4 publications

Constructed Polynomial Windows with High Attenuation of Sidelobes

Constructed Polynomial Windows with High Attenuation of Sidelobes

Use of Triangular Models of Non-Stationary Processes in Modeling Variability of Heart Rhythm

An Effective Method for Analysis of the Diagnostic Features Based on Noisy Electrocardiogram

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