Application of $B$-splines within the method of empirical mode decomposition for expanding a two-dimensional time series into internal modes
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 163-166
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The idea of empirical mode decomposition (EMD) was proposed by N. E Huang as an iterative method of decomposition of a nonlinear and nonstationary function into the sum of components called internal modes. First, EMD was presented as a method for analyzing one-dimensional time series. The method made it possible to extract rapidly oscillating signal components with zero averages superimposed on slow oscillations. In this paper, we describe an algorithm for empirical decomposition of a two-dimensional time series using a $B$-spline in an EMD iterative process.
Keywords:
empirical mode decomposition, two-dimensional time series, $B$-spline, sieving process, rail flaw detection.
@article{INTO_2021_194_a14,
author = {G. N. Sergazy},
title = {Application of $B$-splines within the method of empirical mode decomposition for expanding a two-dimensional time series into internal modes},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {163--166},
publisher = {mathdoc},
volume = {194},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2021_194_a14/}
}
TY - JOUR AU - G. N. Sergazy TI - Application of $B$-splines within the method of empirical mode decomposition for expanding a two-dimensional time series into internal modes JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2021 SP - 163 EP - 166 VL - 194 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2021_194_a14/ LA - ru ID - INTO_2021_194_a14 ER -
%0 Journal Article %A G. N. Sergazy %T Application of $B$-splines within the method of empirical mode decomposition for expanding a two-dimensional time series into internal modes %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2021 %P 163-166 %V 194 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2021_194_a14/ %G ru %F INTO_2021_194_a14
G. N. Sergazy. Application of $B$-splines within the method of empirical mode decomposition for expanding a two-dimensional time series into internal modes. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 163-166. http://geodesic.mathdoc.fr/item/INTO_2021_194_a14/