Abstract
Background. Today, when most processes and phenomena have a periodic structure that is not always homogeneous and depends on a number of irregular events, the classical spectral analysis based on the Fourier transform does not always allow an objective and reliable investigation. A promising alternative to the classical spectral analysis can be a wavelet transform, based on a well-localized function in both time and frequency domains, which allows us to analyze irregular processes. The purpose of the research was to analyze the potentials of the wavelet transform for the analysis of the spectral characteristics of cardiological time series with some heterogeneity; to develop a software application that allows performing wavelet analysis of data and building wavelet spectra, which are illustrative and easy in interpreting the obtained results. Material and methods. 37 cardiological time series were studied. We developed an application for the application package Mathematika 5.0 that allows building and analyzing the wavelet spectra of the studied data. Results. An alternative method for analyzing the spectral characteristics of the studied cardiological time series has been developed and clearly demonstrated. It allows observing the dynamics of the change in periods over the entire observation interval without performing the interval splitting, as would be required by the classical Fourier analysis. Conclusion. For the studied groups of patients the identified periods, found with the help of the wavelet transform have been presented. The advantages of using wavelets over the classical spectral analysis, which in cases of unstable time series does not allow tracking the dynamics of the changing in the data spectrum, have been demonstrated.
Highlights
the classical spectral analysis based on the Fourier transform does
The purpose of the research was to analyze the potentials of the wavelet transform for the analysis
We developed an application for the application package Mathematika 5.0
Summary
Аналогичным образом были исследованы волны первого порядка при значениях периооставшиеся группы пациентов. Выявляемые периоды (масштабы, s) оды: 18-20 – медленные волны первого порядка; 30-38 – мед-. На скалограммах исследуемых временных ности исследовать частотный состав сигналов в рядов максимальные значения вейвлет-коэффи- силу несостоятельности построенных периодоциентов наблюдались на малых значениях мас- грамм, вейвлет-преобразование при правильном штабов. M. Кибернетический анализ процессов управления сердечным ритмом / Р. Г. Введение в анализ данных с применением непрерывного вейвлет-преобразования / В. Н. Практическое применение непрерывного вейвлет-преобразования к анализу временных рядов с выраженной неоднородностью / Н. Н. Сакович // Математическое и компьютерное моделирование систем и процессов : сборник научных статей / Учреждение образования "Гродненский гос. М. Вейвлет-анализ: основы теории и примеры применения / Н. Correlations among time and frequency domain measures of heart period variability two weeks after acute myocardial infarction / J. Malliani [et al.] // Circulation. – 1991. – Vol 84. – P. 482-492
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