Some advantages of non-binary Galois fields for digital signal processing
Moldakhan I. Matrassulova D.K. Shaltykova D.B. Suleimenov I.E.
August 2021Institute of Advanced Engineering and Science
Indonesian Journal of Electrical Engineering and Computer Science
2021#23Issue 2871 - 878 pp.
It is shown that the convenient processing facilities of digital signals that varying in a finite range of amplitudes are non-binary Galois fields, the numbers of which elements are equal to prime numbers. Within choosing a sampling interval which corresponding to such a Galois field, it becomes possible to construct a Galois field Fourier transform, a distinctive feature of which is the exact correspondence with the ranges of variation of the amplitudes of the original signal and its digital spectrum. This favorably distinguishes the Galois Field Fourier Transform of the proposed type from the spectra, which calculated using, for example, the Walsh basis. It is also shown, that Galois Field Fourier Transforms of the proposed type have the same properties as the Fourier transform associated with the expansion in terms of the basis of harmonic functions. In particular, an analogue of the classical correlation, which connected the signal spectrum and its derivative, was obtained. On this basis proved, that the using of the proposed type of Galois fields makes it possible to develop a complete analogue of the transfer function apparatus, but only for signals presented in digital form.
Digital processing , Fourier transform , Galois fields , Transfer functions
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Almaty University of Power Engineering and Telecommunications, Kazakhstan
National engineering Academy of Republic of Kazakhstan, Kazakhstan
Crimean Federal University named by V.I. Vernadsky, Crimea, Simferopol, Ukraine
Almaty University of Power Engineering and Telecommunications
National engineering Academy of Republic of Kazakhstan
Crimean Federal University named by V.I. Vernadsky
10 лет помогаем публиковать статьи Международный издатель
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