Electronic Fourier–Galois Spectrum Analyzer for the Field GF(31)
Abstract
:1. Introduction
2. Methods
3. Results
3.1. Simplifying the Representation of Basis Functions
3.2. Algorithm of the Fourier–Galois Spectrum Analyzer
4. Spectrum Analyzer in the Galois Field GF(31)
4.1. Scheme of Adders and Multipliers by 5 Modulo Number 31
4.2. Test Results of the Proposed Scheme
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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- | 1 | 6 | 5 | 25 | 26 | 30 |
---|---|---|---|---|---|---|
- | - | 5 × 5 × 30 | - | 5 × 5 | 5 × 30 | - |
a4 | 0 | 0 | 0 | 1 | 1 | 1 |
a3 | 0 | 0 | 0 | 1 | 1 | 1 |
a2 | 0 | 1 | 1 | 0 | 0 | 1 |
a1 | 0 | 1 | 0 | 0 | 1 | 1 |
a0 | 1 | 0 | 1 | 1 | 0 | 0 |
m = 1 | 1 | 2 | 3 | 4 | 5 | m = 2 | 1 | 2 | 3 | 4 | 5 |
a4 | 0 | 0 | 0 | 1 | 0 | a4 | 0 | 1 | 0 | 0 | 0 |
a3 | 0 | 0 | 1 | 0 | 0 | a3 | 0 | 0 | 0 | 1 | 0 |
a2 | 0 | 1 | 0 | 0 | 0 | a2 | 1 | 0 | 0 | 0 | 0 |
a1 | 1 | 0 | 0 | 0 | 0 | a1 | 0 | 0 | 1 | 0 | 0 |
a0 | 0 | 0 | 0 | 0 | 1 | a0 | 0 | 0 | 0 | 0 | 1 |
m = 3 | 1 | 2 | 3 | 4 | 5 | m = 4 | 1 | 2 | 3 | 4 | 5 |
a4 | 0 | 0 | 1 | 0 | 0 | a4 | 1 | 0 | 0 | 0 | 0 |
a3 | 1 | 0 | 0 | 0 | 0 | a3 | 0 | 1 | 0 | 1 | 0 |
a2 | 0 | 0 | 0 | 1 | 0 | a2 | 0 | 0 | 1 | 0 | 0 |
a1 | 0 | 1 | 0 | 0 | 0 | a1 | 0 | 0 | 0 | 1 | 0 |
a0 | 0 | 0 | 0 | 0 | 1 | a0 | 0 | 0 | 0 | 0 | 1 |
m = 1 | 1 | 2 | 3 | m = 2 | 1 | 2 | 3 |
---|---|---|---|---|---|---|---|
a4 | 0 | 1 | 0 | a4 | 1 | 0 | 0 |
a3 | 0 | 1 | 0 | a3 | 1 | 0 | 0 |
a2 | 1 | 0 | 0 | a2 | 0 | 1 | 0 |
a1 | 0 | 0 | 0 | a1 | 0 | 0 | 0 |
a0 | 1 | 1 | 1 | a0 | 1 | 1 | 1 |
i | f | F2 | F1 | F3(6) | F3(5) | F3(4) | F3(3) | F3(2) | F3(1) |
---|---|---|---|---|---|---|---|---|---|
1 | 0 | 5 | 30 | 2 | |||||
2 | 0 | 25 | 1 | 4 | |||||
3 | 0 | 1 | 30 | 8 | |||||
4 | 0 | 5 | 1 | 16 | |||||
5 | 0 | 25 | 30 | 1 | |||||
6 | 1 | 1 | 1 | 2 | |||||
7 | 0 | 5 | 30 | 4 | |||||
8 | 0 | 25 | 1 | 8 | |||||
9 | 1 | 1 | 30 | 16 | |||||
10 | 0 | 5 | 1 | 1 | |||||
11 | 1 | 25 | 30 | 2 | |||||
12 | 0 | 1 | 1 | 4 | |||||
13 | 1 | 5 | 30 | 8 | |||||
14 | 1 | 25 | 1 | 16 | |||||
15 | 1 | 1 | 30 | 1 | |||||
16 | 1 | 5 | 1 | 2 | |||||
17 | 1 | 25 | 30 | 4 | |||||
18 | 1 | 1 | 1 | 8 | |||||
19 | 0 | 5 | 30 | 16 | |||||
20 | 1 | 25 | 1 | 1 | |||||
21 | 0 | 1 | 30 | 2 | |||||
22 | 1 | 5 | 1 | 4 | |||||
23 | 0 | 25 | 30 | 8 | |||||
24 | 0 | 1 | 1 | 16 | |||||
25 | 1 | 5 | 30 | 1 | |||||
26 | 0 | 25 | 1 | 2 | |||||
27 | 0 | 1 | 30 | 4 | |||||
28 | 0 | 5 | 1 | 8 | |||||
29 | 0 | 25 | 30 | 16 | |||||
30 | 0 | 1 | 1 | 1 | |||||
Σ | 10 | 6 | 6 | 17 | 17 | 9 | |||
F1 | 1 | 30 | 1 | 30 | 1 | 30 | |||
F1Σ | 10 | 25 | 6 | 14 | 17 | 22 | |||
F2 | 1 | 25 | 5 | 1 | 25 | 5 | |||
F2F1Σ | 10 | 5 | 30 | 14 | 22 | 17 | |||
Z1 | 5 |
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Kadyrzhan, K.; Kaldybekov, D.; Baipakbaeva, S.; Vitulyova, Y.; Matrassulova, D.; Suleimenov, I. Electronic Fourier–Galois Spectrum Analyzer for the Field GF(31). Appl. Sci. 2024, 14, 7770. https://doi.org/10.3390/app14177770
Kadyrzhan K, Kaldybekov D, Baipakbaeva S, Vitulyova Y, Matrassulova D, Suleimenov I. Electronic Fourier–Galois Spectrum Analyzer for the Field GF(31). Applied Sciences. 2024; 14(17):7770. https://doi.org/10.3390/app14177770
Chicago/Turabian StyleKadyrzhan, Kaisarali, Daulet Kaldybekov, Saltanat Baipakbaeva, Yelizaveta Vitulyova, Dinara Matrassulova, and Ibragim Suleimenov. 2024. "Electronic Fourier–Galois Spectrum Analyzer for the Field GF(31)" Applied Sciences 14, no. 17: 7770. https://doi.org/10.3390/app14177770