Method of studying the synchronization of self-sustained oscillations using continuous wavelet analysis of univariant data

Короновский, А. А.; Ponomarenko, V. I.; Прохоров, М. Д.; Hramov, Alexander E.

doi:10.1134/s1063784207090022

Cited by 7 publications

(10 citation statements)

References 29 publications

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“…We will use the recently proposed approach [22,23,24,25] to the analysis of synchronization based on examination of a continuous set of phases defined with the help of the continuous wavelet transform [18,26] …”

Section: Methods Of Detecting Synchronization Using Continuous Wamentioning

confidence: 99%

Detecting synchronization of self-sustained oscillators by external driving with varying frequency

et al. 2006

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We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.

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Section: Methods Of Detecting Synchronization Using Continuous Wamentioning

confidence: 99%

Detecting synchronization of self-sustained oscillators by external driving with varying frequency

et al. 2006

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“…For that purpuse wide variety of methods were developed, including coherence function [74], synchrogram [75,76], coefficient of phase coherency [49], methods based on wavelet transform [77][78][79][80], etc. However, analysis of complex biological objects often requires to consider features of concrete systems, which commonly leads to necessity of making modifications to existing methods or developing new ones.…”

Section: Analysis Of Phase Synchronization Between 01 Hz Oscillationmentioning

confidence: 99%

Method of estimation of synchronization strength between low-frequency oscillations in heart rate variability and photoplethysmographic waveform variability

Kiselev¹,

Anatoly²,

Gridnev³

et al. 2016

Russ. Open Med. J.

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Abstract:This paper describes in detail a new method proposed by authors for quantitative estimation of the strength of synchronization between the low-frequency oscillations (with the main frequency of about 0.1 Hz) in the heart rate variability (HRV) and photoplethysmogram (PPG). Calculation of index value is followed by statistical significance control. The proposed method is applied for the analysis of 1056 pairs of HRV and PPG signals obtained from patients having different clinical status. Methodological recommendations are developed for method application in clinical studies. Keywords: low-frequency oscillations, heart rate variability, photoplethysmogram, baroreflexCite as Kiselev AR, Karavaev AS, Gridnev VI, Prokhorov MD, Ponomarenko VI, Borovkova EI, Shvartz VA, Ishbulatov YM, Posnenkova OM, Bezruchko BP. Method of estimation of synchronization strength between low-frequency oscillations in heart rate variability and photoplethysmographic waveform variability.

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“…Considering the Fourier images for the initial signal O x k and wavelet O also reduces the number of required operations [8,16]. By the convolution theorem, one can simultaneously compute all values of W .n; s/ (n D 0; : : : ; N 1) in the Fourier space for the fixed time scale s using the discrete Fourier transform.…”

Section: Numerical Methods For the Continuous Wavelet Transform Based mentioning

confidence: 98%

“…Equation (2.16) is the standard form of the continuous wavelet transform introduced in the scientific literature [7,12,14,[16][17][18][19][20]. At the end of this section we need also to compare the notation in this section with the one used traditionally in the literature.…”

Section: 4)mentioning

confidence: 97%

“…Other functions are also applied in practice and successfully used in various areas of research. The reader can find additional examples of the mother wavelets as well as ways to construct them, e.g., in [16,[26][27][28][29][30]. In the following chapters of this book, we shall discuss examples of wavelets constructed especially to analyze neurophysiological signals.…”

Section: <mentioning

confidence: 99%

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Brief Tour of Wavelet Theory

Hramov

Короновский

Makarov

et al. 2014

Wavelets in Neuroscience

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In this chapter, the main definitions of wavelet theory are given. To explain the basic ideas of the continuous wavelet transform, we describe a transition from Fourier analysis to wavelets. Mother functions and numerical techniques for implementing the wavelet transform are described. The problem of visualising the results is considered. Finally, features of the discrete wavelet transform are discussed.

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Method of studying the synchronization of self-sustained oscillations using continuous wavelet analysis of univariant data

Cited by 7 publications

References 29 publications

Detecting synchronization of self-sustained oscillators by external driving with varying frequency

Detecting synchronization of self-sustained oscillators by external driving with varying frequency

Method of estimation of synchronization strength between low-frequency oscillations in heart rate variability and photoplethysmographic waveform variability

Brief Tour of Wavelet Theory

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