A.S. Zinchenko1, A.Yu. Burova2

1,2 Moscow Aviation Institute (National Research University) (Moscow, Russia)

1,2 frambe@mail.ru

The issues related to the study of the possibilities of virtual programming of digital counterparts of electronic equipment are considered. The relevance of the study is due to the need to reduce the computational complexity of digital signal processing algorithms for the virtualization of tests of aviation electronic equipment. The purpose of the study is to formalize numerical methods of difference digital filtering with difference coefficients of various orders of magnitude. The methods of mathematical and software modeling of numerical methods were used in the study. The results of the study showed and confirmed the possibility of modeling these filters by directional search and comparative analysis of their difference coefficients. The concept of difference digital filtering, the term «Difference digital filtering» and the concept of such filtering are defined and described. A mathematical model of a recursive difference digital filter is proposed. The numerical method of recursive difference digital filtering of different orders and different orders of difference is formalized. An example of using binary difference coefficients of a recursive RCF is given to replace convolutions of time samples of digital signals and difference coefficients of a digital filter with these reports in order to ensure the construction of a digital filtering algorithm without algorithmic multiplication operations. The results of modeling numerical methods of difference digital filtering with trivial difference coefficients of various difference orders are presented. Mathematical and software modeling of the proposed algorithm for convolution of the sequences of the time samples of the filtered digital signal and the integer coefficients of the difference digital filtering makes it possible to reduce the computational complexity of the hardware and software implementation of digital doubles of the difference digital filters with such coefficients.

Zinchenko A.S., Burova A.Yu. Numerical methods for software modeling of digital algorithms for difference filtering without algorithmic multiplication operations. Achievements of modern radioelectronics. 2025. V. 79. № 7. P. 48–61. DOI: https://doi.org/10.18127/ j20700784-202507-03 [in Russian]

1. Buynachev S.K. Primenenie chislennykh metodov v matematicheskom modelirovanii: Ucheb. posobie. Ekaterinburg: Izdatel'stvo Ural'skogo universiteta. 2014. [in Russian]
2. Pirumov U.G., Gidaspov V.Yu., Ivanov I.E., Reviznikov D.L. i dr. Chislennye metody: Uchebnik i praktikum dlya vuzov. M.: Yurayt. 2023. [in Russian]
3. Burova A.Yu. Metody i ustroystva, pozvolyayushchie umen'shat' chislo operatsiy umnozheniya v algoritmakh tsifrovoy obrabotki signalov. M.: Dobroe slovo i Ko. 2023. [in Russian]
4. Burova A.Yu., Usatenko T.O. Digital Algorithms for the Discrete Frequency Selection of Signals that Do Not Use Algorithmic Multiplication Operations. TEM Journal. 2020. V. 9. № 2. P. 501–506. DOI: https://doi.org/10.18421/TEM92-11.
5. Steshenko V.B. PLIS firmy «ALTERA». Elementnaya baza, sistema proektirovaniya i yazyki opisaniya apparatury. M.: DMK Press. 2016. [in Russian]
6. Vityazev S.V. Tsifrovye protsessory obrabotki signalov. Ucheb. posobie. M.: Goryachaya liniya – Telekom. 2017. [in Russian]
7. Kosichkina T.P., Speranskiy V.S. Tsifrovye signal'nye protsessory i ikh primenenie v sistemakh telekommunikatsiy i elektroniki. M.: Goryachaya liniya – Telekom. 2023. [in Russian]
8. Maslovskaya A.G. Chislennye metody i matematicheskoe modelirovanie. Blagoveshchensk: Amurskiy gos. un-t. 2007. [in Russian]
9. Sharapov D.A. Voprosy sozdaniya chislennykh modeley. Mezhdunarodnyy nauchno-issledovatel'skiy zhurnal. 2024. № 10. DOI: https://doi.org/10.60797/IRJ.2024.148.18. [in Russian]
10. Shinakov Yu.S., Burov Yu.Ya. Raznostnaya tsifrovaya fil'tratsiya s tselochislennymi koeffitsientami. I-ya Mezhdunar. konf. «Tsifrovaya obrabotka signalov i ee primeneniya», 30 iyunya – 3 iyulya 1998 g., Moskva, Rossiya: Doklady: T. II. M.: MTsNTI. 1998. S. 94–99. [in Russian]
11. Burov Yu.Ya. Sintez transversal'nykh raznostnykh fil'trov s tselochislennymi koeffitsientami. Rossiyskoe nauchno-tekhnicheskoe obshchestvo radiotekhniki, elektroniki i svyazi imeni A.S. Popova: LIII Nauchnaya sessiya, posvyashchennaya Dnyu radio: Tezisy dokladov. M.: RNTORES, 1998. S. 238–239. [in Russian]
12. Shinakov Yu.S., Burov Yu.Ya., Burova A.Yu. Teoriya, metody i algoritmy raznostnoy tsifrovoy fil'tratsii. 3-ya Mezhdunarodnaya konferentsiya: «Tsifrovaya obrabotka signalov i ee primenenie», 29 noyabrya – 1 dekabrya 2000 g., Moskva, Rossiya: Doklady: T. 1. M.: MTsNTI. 2000. S. 96–99. [in Russian]
13. Burov Yu.Ya., Burova A.Yu. Teoriya i tsifrovye metody rekurrentnoy raznostnoy fil'tratsii. 3-ya Mezhdunarodnaya konferentsiya: «Tsifrovaya obrabotka signalov i ee primenenie DSPA-2000», 29 noyabrya – 1 dekabrya 2000 g., Moskva, Rossiya: Doklady: T. 3. M.: MTsNTI. 2000. C. 157–160. [in Russian]
14. Burov Yu.Ya., Burova A.Yu. Sintez rekurrentnykh raznostnykh tsifrovykh fil'trov. Rossiyskoe nauchno-tekhnicheskoe obshchestvo radiotekhniki, elektroniki i svyazi imeni A.S. Popova: LV Nauchnaya sessiya, posvyashchennaya Dnyu radio: Tezisy dokladov. M.: RNTORES. 2000. S. 261. [in Russian]
15. Kuz'kin V.S. Raznostnaya tsifrovaya fil'tratsiya. Radiotekhnika. 1983. № 1. S. 52–54. [in Russian]
16. Samarskiy A.A. Vvedenie v teoriyu raznostnykh skhem. M.: Nauka. 1971. [in Russian]
17. Burova A.Yu. Digital signal processing without performing arithmetic multiplication operations. Amazonia Investiga, 2020. V. 9. № 25. P. 200–205.
18. Gold B., Reyder Ch. Tsifrovaya obrabotka signalov: s prilozheniem raboty D. Kayzera «Tsifrovye fil'try». Per. s angl. pod red. A.M. Trakhtmana. M.: Sov. radio. 1973. [in Russian]
19. Rabiner L., Gould B. Teoriya i primenenie tsifrovoy obrabotki signalov. Per. s angl. A.L. Zaytseva i dr. pod red. Yu.N. Aleksandrova. M.: Mir. 1978. [in Russian]
20. Oppengeym A.V., Shafer R.V. Tsifrovaya obrabotka signalov. Per. s angl. V.A. Leksachenko, V.G. Chelpanova pod red. S.Ya. Shatsa. M.: Svyaz'. 1979. [in Russian]
21. Anton'yu A. Tsifrovye fil'try: analiz i proektirovanie. Per. s angl. V.A. Leksachenko, V.G. Chelpanova pod red. S.A. Ponyrko. M.: Radio i svyaz'. 1983. [in Russian]
22. Kappelini V., Konstantinidis A. Dzh., Emiliani P. Tsifrovye fil'try i ikh primenenie. Per. s angl. V.N. Eliseeva. M.: Energoatomizdat. 1983. [in Russian]
23. Khemming R.V. Tsifrovye fil'try. Per. s angl. V.N. Lisina pod red. O.A. Potapova. M.: Nedra. 1987. [in Russian]
24. Burova A.Yu. Teoriya i metodologiya mnogostupenchatogo diskretnogo preobrazovaniya Fur'e bez ispol'zovaniya operatsiy umnozheniya: monografiya. M.: Dobroe slovo i K°. 2023. [in Russian]
25. Milic L.D., Lutovac M.D. Design of multiplierless elliptic IIR halfband filters and Hilbert transformers. Proc. 9th European Signal Processing Conference (EUSIPCO'98), Rhodes, Greece, 8-11 September. 1998. P. 291–294.
26. Milic L.D., Lutovac M.D. Design of multiplierless elliptic IIR filters with a small quantization error. IEEE Trans. Signal Proc. 1999. V. 47. № 2. P. 469–479.
27. Milic L.D., Lutovac M.D. Approximate linear phase multiplierless IIR halfband filter. IEEE Trans. Signal Proc. Lett. 2000. V. 7. № 3. P. 5253.
28. Yli-Kaakinen J., Saramaki T. An algorithm for the design of multiplierless approximately linear-phase lattice wave digital filters. ISCAS. 2000. May. P. 77–80.
29. Milic L.D., Lutovac M.D. Efficient algorithm for the design of high-speed elliptic IIR filters. Int. J. Electron. Commun. (AEU). 2003. V. 57. № 4. P. 255–262.
30. Yli-Kaakinen J., Saramaki T. Systematic algorithm for the design of multiplierless lattice wave digital filters. ISCCSP. 2004. Mar. P. 393–396.
31. Meyer-Baese Uwe. Digital Signal Processing with Field Programmable Gate Arrays. Berlin, Germany: Springer. 2004.