For citation:
Bespalov M. S. Ternary Discrete Wavelet Basis. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 3, pp. 367-377. DOI: 10.18500/1816-9791-2020-20-3-367-377, EDN: TTKRGK
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
31.08.2020
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Language:
Russian
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Article
UDC:
519.72
EDN:
TTKRGK
Ternary Discrete Wavelet Basis
Autors:
Bespalov Mikhail S., Vladimir State University
Abstract:
The discrete version and the basic construction of the ternary multiresolution analysis are given, similar to the binary model case of the Haar multiresolution analysis. Based on the constructed basis, an algorithm similar to the fast Haar transformation is proposed. Typical calculation examples are provided.
Key words:
References:
- Novikov I. Ya., Protasov V. Yu., Skopina M. A. Teoriya vspleskov [Wavelet theory]. Moscow, Fizmatlit, 2005. 616 p. (in Russian).
- Masharsky S. M., Malozemov V. N. Haar spectra of discrete convolutions. Comput. Math. Math. Phys., 2000, vol. 40, no. 6, pp. 914–921.
- Ber M. G., Malozemov V. N. The best formulae for the approximate computation of discrete Fourier transforms. Comput. Math. Math. Phys., 1992, vol. 32, no. 11, pp. 1533– 1544.
- Bespalov M. S. Bernoulli’s discrete periodic functions. Applied Discrete Mathematics, 2019, no. 43, pp. 16–36. DOI: https://doi.org/10.17223/20710410/43/2
- Malozemov V. N., Macharskiy S. M. Osnovy discretnogo garmonicheskogo analiza [Basics of Discrete Harmonic Analysis]. St. Petersburg, Lane, 2012. 304 p. (in Russian).
- Bespalov M. S., Sklyarenko V. A. Diskretnye funktsii Uolsha i ikh prilogeniya [Discrete Walsh Functions and its Applications]. Vladimir, Vladimirskiy gosudarstvennyi universitet, 2014. 68 p. (in Russian).
- Farkov Yu. A. Orthogonal Wavelets on Locally Compact Abelian Groups. Funct. Anal. Appl., 1997, vol. 31, iss. 4, pp. 294–296. DOI: https://doi.org/10.1007/BF02466067
- Lang W. C. Wavelet analysis on the Cantor dyadic group. Housten J. Math., 1998, vol. 24, no. 3, pp. 533–544.
- Lukomskii S. F. Multiresolution analysis on zero-dimensional Abelian groups and wavelets bases. Sb. Math., 2010, vol. 201, no. 5, pp. 669–691. DOI: http://dx.doi.org/10.1070/SM2010v201n05ABEH004088
- Pleshcheva E. A., Chernykh N. I. Construction of orthogonal multiwavelet bases. Proc. Steklov Inst. Math. (Suppl.), 2015, vol. 288, suppl. 1, pp. 162–172. DOI: https://doi.org/10.1134/S0081543815020169
- Farkov Yu. A., Stroganov S. A. The use of discrete dyadic wavelets in image processing. Russian Math. (Iz. VUZ), 2011, vol. 55, no. 7, pp. 47–55. DOI: https://doi.org/10.3103/S1066369X11070073
- Barichev A. A., Lukomskii D. S., Lukomskii S. F. Systems of Scales and Shifts in the Problem Still Image Compression. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 4, pt. 2, pp. 505–510 (in Russian). DOI: https://doi.org/10.18500/1816-9791-2014-14-4-505-510
- Daubechies I. Ten Lestures on Wavelets. SIAM, 1992. 454 p. CBMS-NSR Series in Appl. Math.
- Bespalov M. S. Discrete Chrestenson transform. Probl. Inform. Transm., 2010, vol. 46, iss. 4, pp. 353–375. DOI: https://doi.org/10.1134/S003294601004006X
- Kolmogorov A. N., Fomin S. V. Elementy teorii funktsiy i funktsional’nogo analiza [Elements of the theory of functions and functional analysis]. Moscow, Nauka, 1976. 544 p. (in Russian).
Received:
06.05.2019
Accepted:
31.12.2019
Published:
31.08.2020
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