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All Journal Indonesian Journal of Electrical Engineering and Computer Science
Ibragim E. Suleimenov
Crimean Federal University named by V.I. Vernadsky

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Some advantages of non-binary Galois fields for digital signal processing Inabat Moldakhan; Dinara K. Matrassulova; Dina B. Shaltykova; Ibragim E. Suleimenov
Indonesian Journal of Electrical Engineering and Computer Science Vol 23, No 2: August 2021
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v23.i2.pp871-878

Abstract

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.
New application of non-binary Galois fields Fourier transform: digital analog of convolution theorem Elizaveta S. Vitulyova; Dinara K. Matrassulova; Ibragim E. Suleimenov
Indonesian Journal of Electrical Engineering and Computer Science Vol 23, No 3: September 2021
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v23.i3.pp1718-1726

Abstract

It is shown that the use of the representation of digital signals varying in the restricted amplitude range through elements of Galois fields and the Galois field Fourier transform makes it possible to obtain an analogue of the convolution theorem. It is shown that the theorem makes it possible to analyze digital linear systems in same way that is used to analyze linear systems described by functions that take real or complex values (analog signals). In particular, it is possibile to construct a digital analogue of the transfer function for any linear system that has the property of invariance with respect to the time shift. It is shown that the result obtained has a fairly wide application, in particular, it is of interest for systems in which signal processing methods are combined with the use of neural networks.
Co-Authors Dina B. Shaltykova Dinara K. Matrassulova Dinara K. Matrassulova Elizaveta S. Vitulyova Inabat Moldakhan