DIGITAL DATA PROCESSING BASED ON WAVELET TRANSFORMS

Olga Timoshevskaya, Vladimir Londikov, Dmitry Andreev, Victor Samsonenkov, Tatyana Klets

Abstract


The paper focuses on the main theoretical principles and properties of wavelet transforms. The problem of digital data processing based on wavelet transforms is considered. The analysis and processing of signals and functions that are non-stationary in time and inhomogeneous in space are presented. The authors propose methods of progressive coefficients’ values that combine wavelet decomposition and quantization, the main purpose of which is to convey the most important piece of information about a signal.

 


Keywords


basic wavelet function, discrete (DWT) and continuous (CWT) wavelet transform, scaling function, wavelet transform

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References


S. Verteshev, V. Konevtsov, “Processes control with fuzzy initial information in a complex of software design of digital control systems,” in Environment. Technology. Resources: Proceedings of the 11th International Scientific and Practical Conference on Engineering sciences and production technologies, Rezekne, 2017, vol. III, pp. 332-336.

S. Verteshev, V. Konevtsov, “Direct digital control in a complex of software design of digital control systems,” in Environment. Technology. Resources: Proceedings of the 11th International Scientific and Practical Conference on Engineering sciences and production technologies, Rezekne, 2017, vol. III, pp. 337-342.

Bauman National Library, “Wavelet transform,” 2016. [Online]. Available: https://ru.bmstu.wiki/Вейвлет-преобразование [Accessed: Feb. 27, 2021]. (in Russian)

V. Konevtsov, I. Poletaev, S. Verteshev, “Discrete automatic schemes for ASC TP,” in Environment. Technology. Resources: Proceedings of the 10th International Scientific and Practical Conference on Engineering sciences and production technologies, Rezekne, 2015, vol. I, pp. 67-71.

O. V. Nagornov et al., Wavelet analysis in examples. Moscow: NRNU MEPhI, 2010. (in Russian)

Lossless data compression. Odessa: Odessa National Academy of Telecommunications named after A. S. Popov, 2006. (in Russian)

V. P. Dyakonov, Wavelets. From theory to practice. Moscow: Solon-press, 2010. (in Russian)

R. Gonzalez and R. Woods, Digital Image Processing. Moscow: Technosphere, 2012. (in Russian)

T. E. Krenkel and M. A. Bazhanova, “Quantum Daubechies Wavelet Transform,” T-comm - Telecommunications and Transport, vol. 8, No. 12, pp. 35-40, 2014. (in Russian)

N. K. Smolentsev, Fundamentals of Wavelet Theory. Wavelets in MATLAB. Moscow: DMK Press, 2005. (in Russian)

N. M. Astafieva, “Wavelet analysis: the foundations of the theory and examples of application,” Advances in Physiological Sciences, vol. 166, No. 11, pp. 1145-1170, 1996. (in Russian)

D. Andreev, S. Lyokhin, L. Motaylenko, and S. Verteshev, “Models and algorithms for constructing a formalized description of production technologies,” in Environment. Technology. Resources: Proceedings of the 12th International Scientific and Practical Conference on Information Technologies, Rezekne, 2019, vol. II, pp. 21-27.

I. Antonov, I. Bruttan, D. Andreev, and L. Motaylenko, “The method of automated building of domain ontology,” in Environment. Technology. Resources: Proceedings of the 12th International Scientific and Practical Conference on Information Technologies, Rezekne, 2019, vol. II, pp. 34-37.

D. Andreev, S. Lyokhin, V. Nikolaev, and O. Poletaeva, “Development of software for design ontological representations of production technologies,” in Environment. Technology. Resources: Proceedings of the 12th International Scientific and Practical Conference on Information Technologies, Rezekne, 2019, vol. II, pp. 28-33.

D. Salomon, Data, Image and Sound Compression. Moscow: Technosphere, 2004. (in Russian)

Yu. Taranenko, “Wavelet analysis. Part 1,” 2019. [Online]. Available: https://habr.com/ru/post/451278/ [Accessed: Feb. 27, 2021]. (in Russian)

I. Daubechies, Ten Lectures on Wavelets. Izhevsk: Research Center "Regular and Chaotic Dynamics", 2001. (in Russian)

Wikipedia - the free encyclopedia, “Haar Wavelet,” 2020. [Online]. Available: https://ru.wikipedia.org/wiki/ Вейвлет_Хаара [Accessed: Feb. 27, 2021]. (in Russian)

I. M. Dremin, O. V. Ivanov, and V. A. Nechitailo, “Wavelets and their use,” Advances in Physiological Sciences, vol. 171, No. 5. pp. 465-501, 2001. (in Russian)

V. I. Vorobiev and V. G. Gribunin, Theory and Practice of Wavelet Transform. St. Petersburg: VUS, 1999. (in Russian)

Bauman National Library, “Daubechies wavelets,” 2016. [Online]. Available: https://ru.bmstu.wiki/Вейвлеты_ Добеши [Accessed: Feb. 27, 2021]. (in Russian)




DOI: https://doi.org/10.17770/etr2021vol2.6634

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