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Construction of Generalized Rademacher Functions in Terms of Ternary Logic : Solving the Problem of Visibility of Using Galois Fields for Digital Signal Processing

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Generalized Rademacher functions, constructed as a sequence of elements of Galois fields are intended to find the spectral representation of signals with levels. These functions form a complete basis on the interval corresponding to -1 discrete time intervals and for passing into the classical Rademacher functions. The advantage of such spectra obtained using Galois Fields Fourier Transform is that the range of variation of the spectrum amplitudes remains the same as the range of variation of the original signal, which is modeled on discrete time functions taking values in the Galois field.
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Bibliogr. 30 poz., tab., wykr., rys.
  • Almaty University of Power Engineering and Telecommunications named after Gumarbek Daukeyev, Almaty, Republic of Kazakhstan
  • Almaty University of Power Engineering and Telecommunications named after Gumarbek Daukeyev, Almaty, Republic of Kazakhstan
  • National engineering Academy of Republic of Kazakhstan, Almaty, Kazakhstan
  • [1] S.I. Babaev, A. Bastrychkin, B.V. Kostrov, N.V. Lukina, A.A. Vyugina, E.P. Koroleva, “Aspects of Binary Images Spectral Analysis,” 8th Mediterranean Conference on Embedded Computing (MECO), July 2019.
  • [2] Zulfikar M. Yusuf, Shuja A. Abbasi, A. R. M., “Alamoud. FPGA based processing of digital signals using Walsh analysis,” International Conference on Electrical, Control and Computer Engineering 2011 (InECCE), 21-22 June 2011.
  • [3] Lubomyr Petryshyn. “Applying of the Walsh functions systems in navigation digital data processing,” 2016 4th International Conference on Methods and Systems of Navigation and Motion Control (MSNMC), 18-20 Oct. 2016.
  • [4] D. E. Dutkay, and G. Picioroaga, "Generalized Walsh bases and applications,” Acta applicandae mathematicae, vol. 133(1), pp. 1-18, 2014.
  • [5] R. H. Wang and W. Dan, "Improved Haar and Walsh functions over triangular domains,” Journal of the Franklin Institute, vol. 347(9), pp. 1782-1794, 2010.
  • [6] Zulfikar, Shuja A. Abbasi, A.R.M. Alamoud, “A Novel Complete Set of Walsh and Inverse Walsh Transforms for Signal Processing,” 2011 International Conference on Communication Systems and Network Technologies, June 2011.
  • [7] R.M. Aron, M. Lacruz, R.A. Ryan, A.M. Tonge, "The generalized Rademacher functions,” Note di Matematica, vol. 12, pp.15-25, 1992.
  • [8] H. Mussa, Jonathan D. Tyzack, R. Glen, “Note on the Rademacher-Walsh Polynomial Basis Functions,” Journal of Mathematics Research, 2013.
  • [9] Poolakkaparambil, M., Mathew, J., Jabir, A. M., & Mohanty, S. P., “An investigation of concurrent error detection over binary Galois fields in CNTFET and QCA technologies,” IEEE computer society annual symposium on VLSI, 2012, pp. 141-146
  • [10] Pruss, T., Kalla, P., & Enescu, F., “Equivalence verification of large Galois field arithmetic circuits using word-level abstraction via Gröbner bases,” In Proceedings of the 51st Annual Design Automation Conference, 2014, pp. 1-6.
  • [11] Xiusheng Liu., et al., "Galois LCD codes over finite fields," Elsevier, Finite Fields and Their Applications, vol. 49, pp. 227-242, Jan 2018.
  • [12] Shivashankar S., et al., "A Galois field-based texture representation for face recognition," International Journal of Applied Engineering Research, vol. 13(18), pp. 13460-13465, 2018.
  • [13] Shu Lin, et al., "Iterative soft-decision decoding of Reed-Solomon codes of prime lengths, " IEEE International Symposium on Information Theory (ISIT), pp. 341-345, Aug 2017.
  • [14] Liu, P., et al., "Parameter identification of Reed-Solomon codes based on probability statistics and Galois field Fourier transform, " IEEE Access, vol.7, pp. 33619-33630, Mar 2019.
  • [15] Huang, Q., et al., "Low-complexity encoding of quasi-cyclic codes based on Galois Fourier transform," IEEE Transactions on Communications, vol. 62(6), pp. 1757-1767, Apr 2014.
  • [16] Wu, G., et al., "Blind recognition of BCH code based on Galois field Fourier transform," 2015 International Conference on Wireless Communications & Signal Processing (WCSP), IEEE, pp. 1-4, Oct 2015.
  • [17] Lukasiewicz J., "On Three-Valued Logic // Jan Lukasiewicz. Selected Works," Ed. by L. Borkowski. Amsterdam: North-Holland, pp. 87–88, 1970.
  • [18] Karpenko, A., & Tomova, N., "Bochvar's three-valued logic and literal paralogics: Their lattice and functional equivalence," Logic and Logical Philosophy, 26(2), pp. 207-235, 2017.
  • [19] Schumann, A., "Logical Determinacy versus Logical Contingency. The Case of Łukasiewicz’s Three-valued Logic," Studia Humana, 8(2), pp. 8-15, Dec 2019.
  • [20] Aireti Abulikemu, Abudurusuli Aosiman, Maliyamuguli Maimaiti, Tuerhongjiang Abudukelimu, “The Common Problem of Reasoning Based on Multi-Valued-Logic: An Example of Artificial Neural Network,” CSSE 2020: Proceedings of the 2020 3rd International Conference on Computer Science and Software Engineering, 2019, pp. 186–190.
  • [21] Suleimenov, I. E., et al., "Artificial Intelligence: what is it?," In Proceedings of the 2020 6th International Conference on Computer and Technology Applications, pp. 22-25, Apr 2015.
  • [22] Suleimenov, I. E., et al., "Dialectical understanding of information in the context of the artificial intelligence problems," In IOP Conference Series: Materials Science and Engineering, Vol. 630, No. 1, p. 012007, Oct 2019. https://10.1088/1757-899X/630/1/012007
  • [23] Anil Kumar Singh, “Error detection and correction by Hamming code,” 2016 International Conference on Global Trends in Signal Processing, Information Computing and Communication (ICGTSPICC), Dec. 2016.
  • [24] Rawnaq A. Habeeb, “Coding-Decoding Ternary Logic,” Journal of Electrical and Electronic Engineering, 2014.
  • [25] A. Soltani, Saeed Mohammadi, “A Novel Three Value Logic for Computing Purposes,” International Journal of Information Engineering and Electronic Business, 2013. 2013.V3.341
  • [26] Giniyatullin V.M., Arslanov I.G., Bogdanova P.D., Gabitov R.N., Salikhova M.A., “Methods Of Implementation Of Ternary Logic Functions,” Software for innovative information technologies, pp. 239-254, 2014.
  • [27] Vitulyova, Y. S., Bakirov, A. S., Shaltykova, D. B., & Suleimenov, I. E., “Prerequisites for the analysis of the neural networks functioning in terms of projective geometry,” In IOP Conference Series: Materials Science and Engineering, Vol. 946, No. 1, p. 012001, 2020.
  • [28] Akhat S. Bakirov, Ibragim E. Suleimenov, “On the possibility of implementing artificial intelligence systems based on error-correcting code algorithms,” Journal of Theoretical and Applied Information Technology, 99(1) pp 83-99, 2021.
  • [29] Suleimenov, I., Bakirov, A., & Moldakhan, I., “Formalization of Ternary Logic for Application to Digital Signal Processing,” In Energy Management of Municipal Transportation Facilities and Transport, pp. 26-35, Springer, Cham, 2019.
  • [30] Morris Kline, “Mathematics: The Loss of Certainty,” Oxford University Press, 1980.
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
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