Рус Eng During last 365 days Approved articles: 2000,   Articles in work: 332 Declined articles: 800 
Library
Articles and journals | Tariffs | Payments | Your profile

Back to contents

The selection of continuous wavelet transform basis for finding extrema of biomedical signals
Garmaev Bair Zayatuevich

PhD in Physics and Mathematics

Researcher, Institute of Physical Materials Science, Siberian Branch of the Russian Academy of Sciences

670000, Russia, respublika Buryatiya, g. Ulan-Ude, ul. Sakh'yanovoi, 6, kab. 313

bair.garmaev@gmail.com
Boronoev Vitalii Vasil'evich

Doctor of Technical Science

Head of Laboratory, Institute of Physical Materials Science, Siberian Branch of the Russian Academy of Sciences

670042, Russia, Respublika Buryatiya, g. Ulan-Ude, ul. Sakh'yanovoi, 6, kab. 316

vboronojev2001@mail.ru

Abstract.

The authors consider the problem of choosing a wavelet for its application in a continuous wavelet transformation. The whole advantage of wavelet analysis lies in the possibility of choosing a basis among a large number of wavelets. The choice of the analyzing wavelet is usually determined by what information needs to be extracted from the signal under study. Each wavelet has characteristic features, both in time and in frequency space. Therefore, with the help of different wavelets, it is possible to reveal more fully and emphasize certain properties of the analyzed signal. The choice of the analyzing wavelet function for creating a basis for wavelet transform is one of the issues whose successful solution affects the success of using wavelet analysis in the problem being solved. Bypassing this question repels the beginners in this field of researchers from using wavelet analysis or significantly lends the field of its application. The choice of the wavelet function is especially important for a continuous wavelet transform, where the result of the transformation is a three-dimensional continuous wavelet spectrum. This makes it difficult to analyze it, which is often limited to a visual analysis of the projection of the wavelet spectrum on the scale-time axis. This also complicates the choice of the wavelet function, since when changing the wavelet in the projection of the wavelet spectrum, numerous changes that can not be analyzed sometimes occur.The purpose of this work is to show the method of substantiating the choice of the analyzing wavelet-function for its use in continuous wavelet transformation using the example of the problem of localizing the points of extrema of a digital signal. The work uses continuous wavelet transform. We consider wavelet coefficients on different scales for analyzing the changes not on the wavelet spectrum as a whole, but on its individual parts. The proposed technique shows an algorithm for analyzing continuous wavelet spectra with different wavelet functions in order to evaluate their suitability for searching for extrema. An important point in this technique is the transition from a visual analysis of three-dimensional wavelet spectra to a quantitative analysis of two-dimensional wavelet coefficients on different scales. Such a transition shows how the wavelet analysis works inside three-dimensional wavelet spectra (analyzed primarily visually) and automates signal analysis. This also allows us to numerically estimate the accuracy of finding extrema when using a particular wavelet. As a result, the article shows that the Haar wavelet is the most accurate in the problem of searching for signal extrema by means of continuous wavelet analysis.This method of choosing a basis can be used in problems where an acceptable quantitative estimate of the accuracy of the operation of a continuous wavelet transform is possible. This will allow the authors to analyze three-dimensional wavelet spectra not only qualitatively (visually), but also quantitatively.

Keywords: arterial blood pressure signal, scale, extrema definition, basis selection, wavelet, wavelet analysis, modelling, wavelet Haar, continuous wavelet transform, method

DOI:

10.7256/2454-0714.2018.1.23239

Article was received:

05-06-2017


Review date:

12-06-2017


Publish date:

21-03-2018


This article written in Russian. You can find full text of article in Russian here .

References
1.
Vorob'ev V.I. Teoriya i praktika veivlet-preobrazovaniya / Vorob'ev V.I., Gribunin V.G.-SPb: VUS, 1999.-145 s.
2.
Merkusheva A.V. Klassy preobrazovanii nestatsionarnogo signala v informatsionno-izmeritel'nykh sistemakh. III. Vremya-masshtabnye (veivlet-) preobrazovaniya dlya spektral'no-vremennógo analiza / Merkusheva A.V. // Nauchnoe priborostroenie.-2002.-T. 12.-№ 3.-C. 68–82.
3.
D'yakonov V. P. Veivlety. Ot teorii-k praktike / D'yakonov V. P.-M.: SOLON-R, 2002.-448 s.
4.
Astaf'eva N. M. Veivlet analiz: osnovy teorii i primery primeneniya / Astaf'eva N. M. // Uspekhi fizicheskikh nauk.-1996.-t. 166.-№ 11.-S. 1115-1180.
5.
Boronoev V.V. Osobennosti nepreryvnogo veivlet-preobrazovaniya pul'sovykh signalov / Boronoev V.V., Garmaev B.Z., Lebedintseva I.V. // Optika atmosfery i okeana.-2007.-T.20.-№ 12.-S. 1142-1146.
6.
Boronoev V.V. Metod nepreryvnogo veivlet preobrazovaniya v zadache vydeleniya informativnykh tochek pul'sovogo signala / Boronoev V.V., Garmaev B.Z. // Biomeditsinskie radioelektronika.-2009.-№ 3.-S. 44-49.
7.
Boronoev V.V. Osobennosti veivlet-obrazov pul'sovykh signalov pri narushenii gemodinamiki / Boronoev V.V., Garmaev B.Z. // Izv. VUZov. Fizika.-2010.-T. 53.-Vyp. 9/3.-S. 192-193.
8.
Boronoev V.V. Issledovanie statisticheskoi modeli informativnykh tochek pul'sovoi volny / Boronoev V.V., Garmaev B.Z. // Vestnik Buryatskogo gosudarstvennogo universiteta.-2012.-№ 3.-S. 217-219.
9.
Garmaev B.Z. Chislennoe differentsirovanie biomeditsinskikh signalov s pomoshch'yu veivlet-preobrazovaniya / Garmaev B.Z., Boronoev V.V. // Zhurnal radioelektroniki [elektronnyi zhurnal].-2017.-№2.-URL: http://jre.cplire.ru/jre/feb17/9/text.pdf