Geodesic
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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : 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 = {https://geodesic-test.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  - https://geodesic-test.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 https://geodesic-test.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. https://geodesic-test.mathdoc.fr/item/INTO_2021_194_a14/

[1] De Bor K., Prakticheskoe rukovodstvo po splainam, Radio i svyaz, M., 1985 | MR

[2] Huang N. E., “Introduction to the Hilbert–Huang transform and its related mathematical problems”, Interdisc. Math. Sci., 5 (2005), 1–26 | DOI | MR

[3] Huang N. E., Shen Z., Long R. S., Wu M. C., Shih H. H., Zheng Q., Yen N. C., Tung C. C., Liu H. H., “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis”, Proc. Roy. Soc. London Ser. A., 454 (1998), 903–995 | DOI | MR | Zbl

[4] Riemenschneider S., Liu B., Xu Y., Huang N. E., “$B$-Spline based empirical mode decomposition”, Interdisc. Math. Sci., 5 (2005), 27–55 | DOI | MR

[5] Rilling G., Flandrin P., Goncalves P., Lilly J. M., “Bivariate empirical mode decomposition”, IEEE Signal Process. Lett., 14:2 (2007), 936–939 | DOI

[6] Tanaka T., Mandic D. P., “Complex empirical mode decomposition”, IEEE Signal Process. Lett., 14:2 (2007), 101–104 | DOI