Electronic Fourier–Galois Spectrum Analyzer for the Field GF(31)
Kadyrzhan K. Kaldybekov D. Baipakbaeva S. Vitulyova Y. Matrassulova D. Suleimenov I.
September 2024Multidisciplinary Digital Publishing Institute (MDPI)
Applied Sciences (Switzerland)
2024#14Issue 17
A scheme for the Fourier–Galois spectrum analyzer for the field GF(31) is proposed. It is shown that this analyzer allows for solving a wide enough range of problems related to image processing, in particular those arising in the course of experimental studies in the field of physical chemistry. Such images allow digital processing when divided into a relatively small number of pixels, which creates an opportunity to use Galois fields of relatively small size. The choice of field GF(31) is due to the fact that the number 31 is a Mersenne prime number, which considerably simplifies the algorithm of calculating the Fourier–Galois transform in this field. The proposed scheme of the spectrum analyzer is focused on the use of threshold sensors, at the output of which signals corresponding to binary logic are formed. Due to this fact, further simplification of the proposed analyzer scheme is achieved. The constructiveness of the proposed approach is proven using digital modeling of electronic circuits. It is concluded that when solving applied problems in which an image can be divided into a relatively small number of pixels, it is important to take into account the specificity of particular Galois fields used for their digital processing.
Fourier–Galois spectrum , idempotent algebraic elements , orthogonal bases , phase multiplier , rotating images , spectrum analyzer , threshold sensors
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Institute of Telecommunications and Space Engineering, Almaty University of Power Engineering and Telecommunication Named Gumarbek Daukeev, Almaty, 050013, Kazakhstan
National Engineering Academy of the Republic of Kazakhstan, Almaty, 050010, Kazakhstan
National Scientific Laboratory for the Collective Use of Information and Space Technologies (NSLC IST), JSC “Institute of Digital Engineering and Technology”, Satbayev University, Almaty, 050013, Kazakhstan
Institute of Telecommunications and Space Engineering
National Engineering Academy of the Republic of Kazakhstan
National Scientific Laboratory for the Collective Use of Information and Space Technologies (NSLC IST)
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