Yu. A. Bulgakov1, A.A. Mikheev2

1,2 FSBEI HE «Ryazan State Radio Engineering University named after V.F. Utkin» (Ryazan, Russia)

1 yura.bulgakov.00@gmail.com, 2 maa0312@yandex.ru

Isoline drift suppression algorithms based on complex discrete samples are highly selective for specified spectral zones, but their effectiveness decreases when processing real electrocardiosignals, when discrete samples of the isoline drift signal are subject not only to pulse-amplitude modulation, but also pulse-frequency modulation due to physiological heart rate variability. For the development of such algorithms and the correct assessment of their effectiveness, a test model is needed that reproduces these types of modulation, appropriately reflecting (simulating) these processes take place in real electrocardiosignals. This determines the relevance of the work.

To develop a mathematical model of an electrocardiosignal with double modulation (amplitude-pulse and frequency-pulse) to evaluate the effectiveness of algorithms for preprocessing electrocardiosignals based on the use of complex discrete samples of electrocardiosignal elements followed by filtering the sequence of these samples with a low-pass filter.

A mathematical model of the signal is proposed. It is shown that a double-modulated signal in the low-frequency region (in the zero spectral zone) has an inseparable superposition of the energy of signals of additive isoline drift and heart rate variability. Simulation modeling was carried out using the Mathcad computer algebra system, which confirmed the appearance of spurious spectral components from frequency modulation in the zero spectral zone along with the components of the informative signal. The model makes it possible to independently set the parameters of both types of modulation, forming test sequences with the required spectral characteristics.

The developed model and the obtained spectral estimates can be applied for objective comparison and tuning of trend rejection algorithms in electrocardiographs, including mobile and embedded systems, as well as serve as a basis for creating adaptive filters that take heart rate variability into account.

Bulgakov Yu.A., Mikheev A.A. Modeling of double-modulated signals for investigating the efficiency of electrocardiosignal processing algorithms based on complex discrete samples // Biomedicine Radioengineering. 2026. V. 29. № 5. Р. 85-91. DOI: https://doi.org/ 10.18127/j15604136-202605-13

1. Drozdov D.V. Tekhnicheskie i metodicheskie aspekty registratsii biopotentsialov: vybor elektrodov. Funktsional'naya diagnostika. 2010. № 3. S. 6–11. (in Russian).
2. Rangayyan R.M. Analiz biomeditsinskikh signalov. Prakticheskiy podkhod. Per. s angl. Pod red. A.P. Nemirko. M.: FIZMATLIT. 2007. 440 s. (in Russian).
3. Karasev V.V., Mikheev A.A., Nechaev G.I. Izmeritel'nye sistemy dlya vrashchayushchikhsya uzlov i mekhanizmov. M.: Energoatomizdat. 1996. 176 s. (in Russian).
4. Karasev V.V., Mikheev A.A. Obmen dannymi s vrashchayushchimisya ob"ektami. Staryy Oskol: TNT. 2026. 288 s. (in Russian).
5. Ryabykina G.V., Sobolev A.V. Variabel'nost' ritma serdtsa. M.: «Star'Ko». 1998. 200 s. (in Russian).
6. de Boer R.W., Karemaker J.M., Strackee Jan. Spectrum of a series of point events, generated by the integral pulse frequency modulation model. Medical&Biological&Engineering&Computing. 1985. № 3. P. 138–142.
7. Demina L.V., Mel'nik O.V., Mikheev A.A., Solov'eva V.A. Matematicheskoe opisanie funktsii avtomatizma miokarda. Diagnostika nanomaterialov i nanostruktur. Materialy VI-y Vserossiyskoy shkoly-seminara studentov, aspirantov i molodykh uchenykh. T. III. Ryazan': RGRTU. 2013. S. 227–232. (in Russian).
8. Borisov Yu.P., Penin P.I. Osnovy mnogokanal'noy peredachi informatsii. M.: Svyaz'. 1967. 436 s. (in Russian).
9. Bulgakov Yu., Vitiazeva T., Mikheev A. Research of the Spectrum of a Complex Discrete Samples with Sample Rate Variability. 10th Mediterranean Conference on Embedded Computing (MECO – 2021) Proceedings. Budva, Montenegro. IEEE Catalog Number: CFP2039T-ART. P. 323–326.
10. Bulgakov Yu., Vitiazeva T., Mikheev A. Formation of Complex Discrete Samples of Measuring Signals with a Sampling Period Variability. 11th Mediterranean Conference on Embedded Computing (MECO – 2022) Proceedings. Budva, Montenegro. IEEE Catalog Number: CFP2239T-USB. P. 275–278.
11. Pulse Amplitude Modulation. Elektronnyy resurs. URL: https://www.geeksforgeeks.org/electronics-engineering/pulse-amplitude-modulation/ (data obrashcheniya: 10.03.2026).
12. Kolmogorov A.N., Fomin S.V. Elementy teorii funktsiy i funktsional'nogo analiza. M.: Nauka. 1968. 542 s. (in Russian).