Geodesic
Some issues of improving the quality of noisy periodic signals and numerical estimation of their parameters and characteristics; cluster approach --- statement of problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 1, pp. 41-55.

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

In this paper, the technique of processing and analysis of noisy periodic signals are offered, where signals are recorded at discrete moments of time. The technique includes the two stages: signal quality improvement (processing) with the use of the weighted order statistics filters and the cluster analysis of results of processing. The basic definitions and features of the named type of filtration are listed, as well as formulations and definitions of the cluster analysis are introduced. The above said enables us to state problems of periodic signals analysis. Conclusions concerning the efficiency of the cluster analysis with conditions of using the weighted order statistics filters are proved to be true with the use of results of numerical modeling, where a noisy frequency-modulated signal is employed as a model. 
@article{SJVM_2009_12_1_a3,
     author = {V. I. Znak and O. V. Grachev},
     title = {Some issues of improving the quality of noisy periodic signals and numerical estimation of their parameters and characteristics; cluster approach --- statement of problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {41--55},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a3/}
}
TY  - JOUR
AU  - V. I. Znak
AU  - O. V. Grachev
TI  - Some issues of improving the quality of noisy periodic signals and numerical estimation of their parameters and characteristics; cluster approach --- statement of problem
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2009
SP  - 41
EP  - 55
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a3/
LA  - ru
ID  - SJVM_2009_12_1_a3
ER  - 
%0 Journal Article
%A V. I. Znak
%A O. V. Grachev
%T Some issues of improving the quality of noisy periodic signals and numerical estimation of their parameters and characteristics; cluster approach --- statement of problem
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2009
%P 41-55
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a3/
%G ru
%F SJVM_2009_12_1_a3
V. I. Znak; O. V. Grachev. Some issues of improving the quality of noisy periodic signals and numerical estimation of their parameters and characteristics; cluster approach --- statement of problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 1, pp. 41-55. http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a3/

[1] Laions R., Tsifrovaya obrabotka signalov, Binom, M., 2006

[2] Khelstrom K., Statisticheskaya teoriya obnaruzheniya signalov, Inostrannaya literatura, M., 1963

[3] Torrence C., Comp G.P., “A practical guide to wavelet analysis”, Bulletin of the American Meteorological Society, 79:1 (1998), 61–78 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[4] Baziw E., “Implementation of the principle phase decomposition algorithm”, IEEE Transactions on Geoscience and Remote Sensing, 45:6 (2007), 1775–1785 | DOI

[5] Lin Yin Neuvo Y., “Fast adaptation and performance characteristics of fir-wos hybrid filters”, IEEE Transactions on signal processing, 42:7 (July) (1994), 1610–1628 | DOI

[6] Arce G.R., “A general weighted median filter structure admitting negative weights”, IEEE Transactions on signal processing, 46:12 (December) (1998), 3195–3205 | DOI

[7] Znak V.I., “Sinfazno-vzveshennyi mediannyi filtr i nekotorye voprosy otsenki kachestva ego otklika na chastotno-modulirovannyi signal”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd.-nie. — Novosibirsk, 6:3 (2003), 269–278

[8] Znak V.I., “Co-Phased median filters. Some peculiarities of sweep signal processing”, Mathematical Geology, 37:2 (2005), 207–221 | DOI | Zbl

[9] Akarun L. and Haddad R.A., “Decimated rank order filtering”, IEEE Transactions on signal processing, 42:4 (1994), 835–845 | DOI

[10] Znak V.I., “Sinfazno-vzveshennyi mediannyi filtr: raschet vesov i obrabotka garmonicheskogo signala”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd.-nie. — Novosibirsk, 4:1 (2001), 31–40 | MR

[11] Znak V.I., “One way of organizing N-tap co-phased weighted median filters”, Proc. of the Second IASTED Informational Multi-Conf. on Automation, Control, and Information Technology–Signal and Image Processing (ACIT-SIP) (Novosibirsk, Russia, 2005), 137–143

[12] Venttsel E.S., Teoriya veroyatnostei, Fizmatgiz, M., 1962

[13] Dzhonson N., Lion F., Statistika i planirovanie eksperimenta v nauke i tekhnike. Metody obrabotki dannykh, Mir, M., 1980

[14] Borovikov V., STATISTICA. Iskusstvo analiza dannykh na kompyutere: Dlya professionalov, Piter, SPb., 2003

[15] Prigarin S.M., “Analiz otsenok momenta razladki”, Problemno-orientirovannye vychislitelnye kompleksy, Sb. nauchnykh trudov, Novosibirsk, 1985, 87–92

[16] Nikiforov I.V., “A simple recursive algorithm for diagnosis of abrupt in random signals”, IEEE Transactions on Information Theory, 46:6 (2000), 2740–2746 | DOI | MR | Zbl