# Elimination of Boundary Effects at the Numerical Implementation of Continuous Wavelet Transform to Nonstationary Biomedical Signals

### S. Bozhokin, I. Suslova, D. Tarakanov

#### Abstract

The main objective of the paper is to develop an algorithm improving the situation with boundary effects at the numerical implementation of continuous wavelet transform, what makes it possible to hold down important information in the study of many nonstationary biological signals. As a basis for the research, we propose the mathematical model of nonstationary signal (NS) with a complex amplitude variation in time. Such signals show peaks near the beginning and end of the observation period. The model leads to the analytical expression for continuous wavelet transform (CWT). Thus, we get to know how boundary effects relate to the finiteness in time of the mother wavelet function. To avoid boundary effects arising at the procedure of numerical wavelet transform, we develop the algorithm of signal time shift (STS). The results of analytical solution and numerical CWT calculation with and without the use of STS show the benefit of using STS in the processing of nonstationary signals. We have applied the technique to the study of nonstationary heart tachogram and discovered heart activity bursts in different spectral ranges, which appear and disappear at different time moments.

Download#### Paper Citation

#### in Harvard Style

Bozhokin S., Suslova I. and Tarakanov D. (2019). **Elimination of Boundary Effects at the Numerical Implementation of Continuous Wavelet Transform to Nonstationary Biomedical Signals**.In *Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOSIGNALS,* ISBN 978-989-758-353-7, pages 21-32. DOI: 10.5220/0007254900210032

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOSIGNALS,

TI - Elimination of Boundary Effects at the Numerical Implementation of Continuous Wavelet Transform to Nonstationary Biomedical Signals

SN - 978-989-758-353-7

AU - Bozhokin S.

AU - Suslova I.

AU - Tarakanov D.

PY - 2019

SP - 21

EP - 32

DO - 10.5220/0007254900210032

#### in Bibtex Style

@conference{biosignals19,

author={S. Bozhokin and I. Suslova and D. Tarakanov},

title={Elimination of Boundary Effects at the Numerical Implementation of Continuous Wavelet Transform to Nonstationary Biomedical Signals},

booktitle={Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOSIGNALS,},

year={2019},

pages={21-32},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007254900210032},

isbn={978-989-758-353-7},

}