The Methods of Choosing the Wavelets for One Dimensional Signal Processing

2019;
: pp. 84 - 90
Authors:
1
Lviv Polytechnic National University

The paper describes the problems of the effectiveness increasing in the selection of base functions for the processing of different types of one-dimensional signals in the wavelet domain. The efficiency of representing signals in the wavelet domain has been shown; their analysis and processing are related to the choice of base functions. The basic methods and algorithms for selecting base functions are defined, in which the choice of optimal wavelets has been carried out according to a particular criterion for certain types of signals. Methods have been presented for assessing the efficiency of the choice of base wavelets by the criterion for the ratio of the energy of the wavelet coefficients to the entropy of energy distribution of wavelet coefficients, the criterion for estimating the correlation coefficient, and the information criterion. The universal index of quality of the signal has been proposed and substantiated for the first time as a new criterion for choosing a wavelet and the method has been improved for the choice of base wavelets using a genetic algorithm according to the universal signal quality index criterion. The method of multi-criteria optimization of the choice of base wavelet for the processing one-dimensional non-periodic signals based on the tools of fuzzy logic has been proposed and developed, which made it possible to improve the efficiency of signal processing.

[1] Nakonechnyy A. Y., Teoriya malokhvylovoho (wavelet) peretvorennya ta yiyi zastosuvannya. Lviv: Feniks, 2001. 278p.

[2] Smolentsev N. K. Osnovy teorii veyvletov. Veyvlety v MATLAB. Moskva: DMK Press, 2014. 628 p.

[3] Cunha, Caio F. and Carvalho, André and Petraglia, M.R. and Lima, Antonio C. S. An improved scale dependent wavelet selection for data denoising of partial discharge measurement. Proceedings of IEEE International Conference on Solid Dielectrics, ICSD, 2013. Pp. 100-104.

[4] Yang, Q.; Wang, J. Multi-Level Wavelet Shannon Entropy- Based Method for Single-Sensor Fault Location. Entropy. 17, 2015. Pp. 7101-7117.
https://doi.org/10.3390/e17107101

[5] J. Rafiee, M.A. Rafiee, N. Prause, M.P. Schoen. Wavelet basis functions in biomedical signal processing. Expert Systems with Applications. 38(5), 2011. Pp. 6190-620.
https://doi.org/10.1016/j.eswa.2010.11.050

[6] T.M. Cover; J.A. Thomas. Elements of Information Theory, 2nd ed. Wiley-Interscience: Hoboken, NJ, USA, 2006.

[7] N. Wu, Y.Q. Wei. Research on Wavelet Energy Entropy and its application to harmonic detection in power system. International Journal of Applied Physics and Mathematics. 3(1), 2013. Pp. 31-33.
https://doi.org/10.7763/IJAPM.2013.V3.168

[8] H. Hong, Y. Tan, Y. Wang. Optimal base wavelet selection for ECG noise reduction using a Comprehensive Entropy Criterion. Entropy. Vol. 17, Issue 9, 2015. Pp. 6093-6109.
https://doi.org/10.3390/e17096093

[9] Dyakonov V. P. Veyvlety. Ot teorii k praktike. Moskva: SOLON-R, 2002. 448 p.

[10] I. Lagun, A. Nakonechnyi. Selection of wavelet basis for the effectiveness processing of signals. Vestnik Brestskogo gosudarstvennogo tekhnicheskogo universiteta, №5, 2016. Pp. 69-73.

[11] Shtoyyer R. Mnogokriterialnaya optimizatsiya. Teoriya, vychisleniya, i prilozheniya. Moskva: Radio i svyaz, 1992. 504 p.

[12] Saati T. Prinyatiye resheniy. Metod analiza iyerarkhiy. Moskva: Radio i svyaz, 1993. 320 p.

[13] Shtovba S. D. Proyektirovaniye nechetkikh sistem sredstvami MATLAB. Moskva: Goryachaya liniya - Telekom, 2007. 288 p.

[14] Lotfi A Zadeh.. Fuzzy Sets. Information and Control, №8, 1965. Pp. 338-353.
https://doi.org/10.1016/S0019-9958(65)90241-X

[15] Z. Wang, A. C. Bovik. A universal image quality index. IEEE Signal Processing Letters, vol. 9, № 3, 2002. Pp. 81-84.
https://doi.org/10.1109/97.995823

[16] I. I. Lahun, A. Y. Nakonechnyy, R. I. Stakhiv. Vykorystannya universalnoho indeksu yakosti syhnalu pry vybori optymalnykh malokhvylovykh bazovykh funktsiy. Materialy 3-yi Mizhnarodnoyi konferentsiyi z avtomatychnoho upravlinnya ta informatsiynykh tekhnolohiy, ICACIT-2015, Kyiv, 11-13 December 2015. Kyiv, 2015. Pp. 132-135.

[17] Burakov M. V. Geneticheskiy algoritm: teoriya i praktika: uchebnoye posobiye. Sankt Peterburg: GUAP, 2008. 164 p.

[18] Lahun I. I., Nakonechnyy R. A. Optymizatsiya poshuku bazovykh malokhvylovykh funktsiy z vykorystannyam henetychnoho alhorytmu. Visnyk Natsionalnoho universytetu "Lvivska politekhnika". Avtomatyka, vymiryuvannya ta keruvannya. Lviv: NU "Lvivslka politekhnika", 2015. № 821. Pp. 30-36.