Назва:	Mathematical, Algorithmic and Software Support for Phonocardiographic Signal Processing to Detect Mitral Insufficiency of Human Heart Valves
Автори:	Yavorska, Evhenia Khvostivskyi, Mykola Kinash, Roman Boyko, Roman
Приналежність:	ТНТУ
Бібліографічний опис:	Khvostivskyi Mykola, Yavorska Evhenia, Kinash Roman, Boyko Roman. Mathematical, Algorithmic and Software Support for Phonocardiographic Signal Processing to Detect Mitral Insufficiency of Human Heart Valves. 3rd International Workshop on Information Technologies: Theoretical and Applied Problems (ITTAP-2023). CEUR Workshop Proceedings. Ternopil, Ukraine, Opole, Poland, November 22-24, 2023. pp. 350-357. ISSN 1613-0073
Bibliographic description:	Khvostivskyi Mykola, Yavorska Evhenia, Kinash Roman, Boyko Roman. Mathematical, Algorithmic and Software Support for Phonocardiographic Signal Processing to Detect Mitral Insufficiency of Human Heart Valves. 3rd International Workshop on Information Technologies: Theoretical and Applied Problems (ITTAP-2023). CEUR Workshop Proceedings. Ternopil, Ukraine, Opole, Poland, November 22-24, 2023. pp. 350-357. ISSN 1613-0073
Конференція/захід:	3rd International Workshop on Information Technologies: Theoretical and Applied Problems (ITTAP-2023)
Дата публікації:	2024
Дата подання:	2023
Дата внесення:	18-лют-2024
Видавництво:	CEUR Workshop Proceedings
Країна (код):	UA
Місце видання, проведення:	CEUR Workshop Proceedings. Ternopil, Ukraine, Opole, Poland, November 22-24, 2023.
Ідентифікатор ORCID:	https://orcid.org/0000-0002-2405-4930 https://orcid.org/0000-0001-6341-1710 https://orcid.org/0009-0007-0904-595X https://orcid.org/0000-0003-3671-9917
УДК:	519.216 612.171.3 004.4
Діапазон сторінок:	350-357
Опис:	Mathematical support for phonocardiographic signal processing has been developed based on a mathematical model in the form of a periodically correlated stochastic process and a component processing method. On the basis of mathematical support, algorithmic and software was developed in the Matlab environment for automated systems of computer diagnostics of the functional state of the valves of the human heart when mitral insufficiency is detected.
Зміст:	1. Introduction 2. Mathematical support for phonocardiographic signal processing 3. Algorithmic support for phonocardiographic signal processing 4. Software and results of phonocardiographic signal processing 5. Conclusions 6. References
URI (Уніфікований ідентифікатор ресурсу):	http://elartu.tntu.edu.ua/handle/lib/44515
ISSN:	1613-0073
Власник авторського права:	© Khvostivskyi Mykola, Yavorska Evhenia, Kinash Roman, Boyko Roman, 2024 © Khvostivskyi Mykola, Yavorska Evhenia, Kinash Roman, Boyko Roman, 2024 © Khvostivskyi Mykola, Yavorska Evhenia, Kinash Roman, Boyko Roman, 2024
URL-посилання пов’язаного матеріалу:	https://ceur-ws.org/Vol-3628/short19.pdf http://elartu.tntu.edu.ua/handle/lib/44247
Перелік літератури:	[1] Baumgartner H, Falk V, Bax JJ, De Bonis M, Hamm C, Holm JP, et al. ESC/EACTS Guidelines for the management of valvular heart disease. Eur Heart J. 2017;38(36): 2739–2791. Available from: doi: 10.1093/eurheartj/ehx391. [2] Dal-Bianco JP, Aikawa E, Bischoff J, et al. Myocardial infarction alters adaptation of the tethered mitral valve. J Am Coll Cardiol. 2016; 67(3): 275–287. doi:10.1016/j.jacc.2015.10.092. [3] Deferm S, Bertrand PB, Verbrugge FH, et al. Atrial functional mitral regurgitation: JACC review topic of the week. J Am Coll Cardiol. 2019;73(19):2465–2476. doi:10.1016/j.jacc.2019.02.061. [4] Deferm S, Bertrand PB, Verhaert D, et al. Mitral annular dynamics in AF versus sinus rhythm: Novel insights into the mechanism of AFMR. JACC Cardiovasc Imaging. 2021;S1936–878X(21)00440-X. doi:10.1016/j. jcmg.2021.05.019. [5] Donal, E; Panis, V (October 2021). "Interaction between mitral valve apparatus and left ventricle. Functional mitral regurgitation: A brief state-of-the-art overview". Advances in Clinical and Experimental Medicine. 30 (10): 991–997. doi:10.17219/acem/143324. PMID 34714608. S2CID 240154628. [6] Gertz ZM, Raina A, Saghy L, et al. Evidence of atrial functional mitral regurgitation due to atrial fibrillation: Reversal with arrhythmia control. J Am Coll Cardiol. 2011;58(14):1474–1481. doi:10.1016/j.jacc.2011.06.032. [7] Grayburn PA, Sannino A, Packer M. Proportionate and disproportionate functional mitral regurgitation: A new conceptual framework that reconciles the results of the MITRA-FR and COAPT trials. JACC Cardiovasc Imaging. 2019;12(2):353–362. doi:10.1016/j.jcmg.2018.11.006. [8] Eng MH, Wang DD. Transseptal transcatheter mitral valve replacement for post- surgical mitral failures. Intervent Cardiol Rev. 2018;13(2): 77–80. Available from: doi: 10.15420/icr.2017:16:3. [9] Iung B, Baron G, Butchartv EG, Delahaye F, Gohlke-Baerwolf CW, Leavang OW, et al. A prospective survey of patients with valvular heart disease in Europe: The Euro Heart Survey on Valvular Heart Disease. Eur Heart J. 2003;24: 1231– 1243. Available from: doi: 10.1016/50195-668X(03)00201-X. [10] Kang DH, Park SJ, Shin SH, et al. Angiotensin receptor neprilysin inhibitor for functional mitral regurgitation. Circulation. 2019;139(11):1354–1365. doi:10.1161/CIRCULATIONAHA.118.037077. [11] Levine RA, Hagege AA, Judge DP, et al. Mitral valve disease: Morphology and mechanisms. Nat Rev Cardiol. 2015;12(12):689–710. doi:10.1038/nrcardio.2015.161. [12] Madesis A, Tsakiridis K, Zarogoulidis P, Katsikogiannis N, Machairiotis N, Kougioumtzi I, et al. Review of mitral valve insufficiency: repair or replacement. J Thorac Dis. 2014;6(1): 39–51. Available from: doi: 10.3978/j.issn.2072- 1439.2013.10.20. [13] Melillo E, Ancona F, Buzzatti N, Denti P, Agricola E. A challenging mitral valve anatomy for percutaneous repair with MitraClip: Cleft posterior leaflet. Eur Heart J Cardiovasc Imaging. 2019;20(12):1433–1434. doi:10.1093/ehjci/jez175. [14] Marsit O, Clavel MA, Cote-Laroche C, et al. Attenuated mitral leaflet enlargement contributes to functional mitral regurgitation after myocardial infarction. J Am Coll Cardiol. 2020;75(4):395–405. doi:10.1016/j.jacc.2019.11.039. [15] Sweeney J, Dutta T, Sharma M, et al. Variations in mitral valve leaflet and scallop anatomy on 3-dimensional transesophageal echocardiography. J Am Soc Echocardiogr. 2021;S0894–7317(21)00598-8. doi:10.1016/j.echo.2021.07.010. [16] Stone GW, Lindenfeld J, Abraham WT, et al. Transcatheter mitral-valve repair in patients with heart failure. N Engl J Med. 2018;379(24):2307–2318. doi:10.1056/NEJMoa1806640. [17] Gianelly, R. E., Popp, R. L. and Hultgren, H. N. (1970). Heart sounds in patients with homograft replacement of the mitral valve. Circulation, 42, 309. 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Rajba, Vector of diagnostic features in the form of decomposition coefficients of statistical estimates using a cyclic random process model of cardiosignal. Proceedings of the 2019 10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2019, 1, pp. 298–303. doi: 10.1109/IDAACS.2019.8924398. [22] Dragan Yaroslav P., Osukhivskaya G.M. Description of sound cardiosignals by periodically correlated random process model. Journal of Automation and Information Sciences. Volume 31, Issue 7-9, 1999, pp. 59-63. doi: 10.1615/JAutomatInfScien.v31.i7-9.100. ISSN: 10642315. [23] Dragan Ya. P., Osukhivska H. M. Invarianty tonalnoho syhnalu na pidstavi yoho modeli u vyhliadi periodychno korelovanoho vypadkovoho protsesu // Visnyk Derzhavnoho universytetu “Lvivska politekhnika”. Lviv vyd-vo Derzh. un-tu “Lvivska politekhnika”. 1998. Vol.1, №337. P. 164-166. [in Ukrainian]. 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P.263-272. ISSN 1613-0073. [27] Hvostivska L., Hvostivskyy M. (2017) Veryfikatsiia synfaznoho ta komponentnoho metodiv analizu pulsovoho syhnalu. Materials of ⅩⅩ Conference TNTU I. Puluj (Tern., 17-18 May 2017), pp. 137-138 [in Ukrainian]. [28] Khvostivska L.V. Mathematical model and methods of pulse signal analysis to increase the informativeness of photoplethysmographic systems: dissertation for obtaining the scientific degree of candidate of technical sciences by specialty 05.01.02 / Liliya Volodymyrivna Khvostivska. Ternopil: TNTU, 2021. 177 p. [29] Khvostivska L., Uniyat S., Khvostivskyi M., Yavorskyi I. Mathematical Support Verification of Methods, Algorithms and Software Processing of Pulse Signals under Physical Load in Computer Diagnostic Systems. Proceedings of the XXVIII International Scientific and Practical Conference. Melbourne, Australia. 2023. Pp. 185-190. ISBN 979-8-89074-574-3. DOI: 10.46299/ISG.2023.1.28. [30] Khvostivska L., Khvostivskyi M., Dediv I., Yatskiv V., Palaniza Y. Method, Algorithm and Computer Tool for Synphase Detection of Radio Signals in Telecommunication Networks with Noises. Proceedings of the 1st International Workshop on Computer Information Technologies in Industry 4.0 (CITI 2023). CEUR Workshop Proceedings. Ternopil, Ukraine, June 14-16, 2023. P.173-180. ISSN 1613-0073. [31] Palianytsia Yu. B. Suchasni pidkhody do opratsiuvannia fonokardiosyhnalu ta matematychna model yoho u vyhliadi periodychno korelovanoho vypadkovoho protsesu // Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky, 2016. Vyp. 2(235). S. 90–93. [in Ukrainian]. [32] Palaniza Y., Yavorska E., Shadrina H., Dediv L. (2018) Phonocardiosignal as a periodically correlated stochastic process preprocessing algorithm structure grounding. Scientific Journal of TNTU (Tern.), vol. 91, no 3, pp. 143-152. [33] Palaniza Y.B., Shadrina H.M., Khvostivskiy M.O., Dediv L.Ye., Dozorska O.F. Main theoretical basis of biosignals modeling. Znanstvena misel. Slovenia. 2018. №16. P. 39-44Wang, Xin, Tapani Ahonen, and Jari Nurmi. "Applying CDMA technique to network-on-chip." IEEE transactions on very large scale integration (VLSI) systems 15.10 (2007): 1091-1100. [34] Palaniza Y., Franchevska H. (2018) Enerhetychni aspekty obrobky biosyhnaliv u kardiolohichnii praktytsi [Energy aspects of biosignals processing in cardiology practice]. Book of abstract of the Ⅶ International scientific and technical conference of young researchers and students "Current issues in modern technologies" (Tern., 28-29 November 2018), vol. 3, pp. 243 [in Ukrainian]. [35] Osukhivska H. M. Matematychna model tonovoho syhnalu dlia diahnostyky stanu klapaniv sertsia liudyny: avtoref. dys. na zdobuttia nauk, stupenia kand. tekhn. nauk: 01.05.02 / H.M. Osukhivska. Ternopil, 1999. 20 p. [in Ukrainian]. [36] H. Osuhivs'ka and I. Kyslak, "Random processes statistic application for cardiosignals characteristics determination," MMET '96. VIth International Conference on Mathematical Methods in Electromagnetic Theory. Proceedings, Lviv, Ukraine, 1996, pp. 264-266, doi: 10.1109/MMET.1996.565708. [37] Osukhivska H. M. Matematychna model porodzhennia tonovoho syhnalu u vyhliadi relaksatsiinoho multypulsatora. Materialy 6-oi nauk. konf. TDTU imeni Ivana Puliuia. Ternopil: TDTU. 2002. P.9. [in Ukrainian]. [38] Khvostivska L., Khvostivskyy M., Dunetc V., Dediv I. Mathematical and Algorithmic Support of Detection Useful Radiosignals in Telecommunication Networks. Proceedings of the 2nd International Workshop on Information Technologies: Theoretical and Applied Problems (ITTAP 2022). Ternopil, Ukraine, November 22-24, 2022. P.314-318. ISSN 1613-0073. [39] I. V. Lytvynenko; P. O. Maruschak; S. A. Lupenko; Yu. I. Hats; A. Menou; S. V. 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References:	[1] Baumgartner H, Falk V, Bax JJ, De Bonis M, Hamm C, Holm JP, et al. ESC/EACTS Guidelines for the management of valvular heart disease. Eur Heart J. 2017;38(36): 2739–2791. Available from: doi: 10.1093/eurheartj/ehx391. [2] Dal-Bianco JP, Aikawa E, Bischoff J, et al. Myocardial infarction alters adaptation of the tethered mitral valve. J Am Coll Cardiol. 2016; 67(3): 275–287. doi:10.1016/j.jacc.2015.10.092. [3] Deferm S, Bertrand PB, Verbrugge FH, et al. Atrial functional mitral regurgitation: JACC review topic of the week. J Am Coll Cardiol. 2019;73(19):2465–2476. doi:10.1016/j.jacc.2019.02.061. [4] Deferm S, Bertrand PB, Verhaert D, et al. Mitral annular dynamics in AF versus sinus rhythm: Novel insights into the mechanism of AFMR. JACC Cardiovasc Imaging. 2021;S1936–878X(21)00440-X. doi:10.1016/j. jcmg.2021.05.019. [5] Donal, E; Panis, V (October 2021). "Interaction between mitral valve apparatus and left ventricle. Functional mitral regurgitation: A brief state-of-the-art overview". Advances in Clinical and Experimental Medicine. 30 (10): 991–997. doi:10.17219/acem/143324. PMID 34714608. S2CID 240154628. [6] Gertz ZM, Raina A, Saghy L, et al. Evidence of atrial functional mitral regurgitation due to atrial fibrillation: Reversal with arrhythmia control. J Am Coll Cardiol. 2011;58(14):1474–1481. doi:10.1016/j.jacc.2011.06.032. [7] Grayburn PA, Sannino A, Packer M. Proportionate and disproportionate functional mitral regurgitation: A new conceptual framework that reconciles the results of the MITRA-FR and COAPT trials. JACC Cardiovasc Imaging. 2019;12(2):353–362. doi:10.1016/j.jcmg.2018.11.006. [8] Eng MH, Wang DD. Transseptal transcatheter mitral valve replacement for post- surgical mitral failures. Intervent Cardiol Rev. 2018;13(2): 77–80. Available from: doi: 10.15420/icr.2017:16:3. [9] Iung B, Baron G, Butchartv EG, Delahaye F, Gohlke-Baerwolf CW, Leavang OW, et al. A prospective survey of patients with valvular heart disease in Europe: The Euro Heart Survey on Valvular Heart Disease. Eur Heart J. 2003;24: 1231– 1243. Available from: doi: 10.1016/50195-668X(03)00201-X. [10] Kang DH, Park SJ, Shin SH, et al. Angiotensin receptor neprilysin inhibitor for functional mitral regurgitation. Circulation. 2019;139(11):1354–1365. doi:10.1161/CIRCULATIONAHA.118.037077. [11] Levine RA, Hagege AA, Judge DP, et al. Mitral valve disease: Morphology and mechanisms. Nat Rev Cardiol. 2015;12(12):689–710. doi:10.1038/nrcardio.2015.161. [12] Madesis A, Tsakiridis K, Zarogoulidis P, Katsikogiannis N, Machairiotis N, Kougioumtzi I, et al. Review of mitral valve insufficiency: repair or replacement. J Thorac Dis. 2014;6(1): 39–51. Available from: doi: 10.3978/j.issn.2072- 1439.2013.10.20. [13] Melillo E, Ancona F, Buzzatti N, Denti P, Agricola E. A challenging mitral valve anatomy for percutaneous repair with MitraClip: Cleft posterior leaflet. Eur Heart J Cardiovasc Imaging. 2019;20(12):1433–1434. doi:10.1093/ehjci/jez175. [14] Marsit O, Clavel MA, Cote-Laroche C, et al. Attenuated mitral leaflet enlargement contributes to functional mitral regurgitation after myocardial infarction. J Am Coll Cardiol. 2020;75(4):395–405. doi:10.1016/j.jacc.2019.11.039. [15] Sweeney J, Dutta T, Sharma M, et al. Variations in mitral valve leaflet and scallop anatomy on 3-dimensional transesophageal echocardiography. J Am Soc Echocardiogr. 2021;S0894–7317(21)00598-8. doi:10.1016/j.echo.2021.07.010. [16] Stone GW, Lindenfeld J, Abraham WT, et al. Transcatheter mitral-valve repair in patients with heart failure. N Engl J Med. 2018;379(24):2307–2318. doi:10.1056/NEJMoa1806640. [17] Gianelly, R. E., Popp, R. L. and Hultgren, H. N. (1970). Heart sounds in patients with homograft replacement of the mitral valve. Circulation, 42, 309. [18] Lim, Eric; Ali, Ziad A; Barlow, Clifford W; Hosseinpour, A Reza; Wisbey, Christopher; Charman, Susan C; Wells, Francis C; Barlow, John B; (2002) Determinants and assessment of regurgitation after mitral valve repair. The Journal of thoracic and cardiovascular surgery, 124 (5). pp. 911-917. ISSN 0022-5223 DOI: https://doi.org/10.1067/mtc.2002.125341. [19] Jun Heum Yon, Song Ook Han, Yun Hee Lim, Kye Min Kim, Youn Suk Lee, Ki Hyuk Hong. (2000). Experience of Phonocardiogram during the Mitral Valve Replacement. Korean Journal of Anesthesiology. 39(2):275-277. DOI: https://doi.org/10.4097/kjae.2000.39.2.275. [20] Dragan Ya.P. Enerhetychna teoriia liniinykh modelei stokhastychnykh syhnaliv. Lviv: Tsentr stratehichnykh doslidzhen eko- bio- tekhnichnykh system, 1997. 361p. [in Ukrainian]. . Martsenyuk, A. Sverstiuk, A. Klos-Witkowska, A. Horkunenko, S. Rajba, Vector of diagnostic features in the form of decomposition coefficients of statistical estimates using a cyclic random process model of cardiosignal. Proceedings of the 2019 10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS 2019, 1, pp. 298–303. doi: 10.1109/IDAACS.2019.8924398. [22] Dragan Yaroslav P., Osukhivskaya G.M. Description of sound cardiosignals by periodically correlated random process model. Journal of Automation and Information Sciences. Volume 31, Issue 7-9, 1999, pp. 59-63. doi: 10.1615/JAutomatInfScien.v31.i7-9.100. ISSN: 10642315. [23] Dragan Ya. P., Osukhivska H. M. Invarianty tonalnoho syhnalu na pidstavi yoho modeli u vyhliadi periodychno korelovanoho vypadkovoho protsesu // Visnyk Derzhavnoho universytetu “Lvivska politekhnika”. Lviv vyd-vo Derzh. un-tu “Lvivska politekhnika”. 1998. Vol.1, №337. P. 164-166. [in Ukrainian]. [24] Dunets V.L., Khvostivskyi M.O., Sverstiuk A.S., Khvostivska L.V. Matematychne ta alhorytmichno-prohramne zabezpechennia opratsiuvannia elektrokadiosyhnaliv pry fizychnomu navantazhenni u kardiodiahnostychnykh systemakh: naukova monohrafiia. Lviv: Vydavnytstvo «Mahnoliia - 2006», 2022. 136 p. [in Ukrainian]. [25] Hvostivska L.V., Osukhivska H.M., Hvostivskyy M.O., Shadrina H.M., Dediv I.Yu. Development of methods and algorithms for a stochastic biomedical signal period calculation in medical computer diagnostic systems. Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, (79), pp. 78-84. doi: 10.20535/RADAP.2019.79.78-84. [26] Franchevska H., Khvostivskyi M., Dozorskyi V., Yavorska E., Zastavnyy O. The Method and Algorithm for Detecting the Fetal ECG Signal in the Presence of Interference. Proceedings of the 1st International Workshop on Computer Information Technologies in Industry 4.0 (CITI 2023). CEUR Workshop Proceedings. Ternopil, Ukraine, June 14-16, 2023. P.263-272. ISSN 1613-0073. [27] Hvostivska L., Hvostivskyy M. (2017) Veryfikatsiia synfaznoho ta komponentnoho metodiv analizu pulsovoho syhnalu. Materials of ⅩⅩ Conference TNTU I. Puluj (Tern., 17-18 May 2017), pp. 137-138 [in Ukrainian]. [28] Khvostivska L.V. Mathematical model and methods of pulse signal analysis to increase the informativeness of photoplethysmographic systems: dissertation for obtaining the scientific degree of candidate of technical sciences by specialty 05.01.02 / Liliya Volodymyrivna Khvostivska. Ternopil: TNTU, 2021. 177 p. [29] Khvostivska L., Uniyat S., Khvostivskyi M., Yavorskyi I. Mathematical Support Verification of Methods, Algorithms and Software Processing of Pulse Signals under Physical Load in Computer Diagnostic Systems. Proceedings of the XXVIII International Scientific and Practical Conference. Melbourne, Australia. 2023. Pp. 185-190. ISBN 979-8-89074-574-3. DOI: 10.46299/ISG.2023.1.28. [30] Khvostivska L., Khvostivskyi M., Dediv I., Yatskiv V., Palaniza Y. Method, Algorithm and Computer Tool for Synphase Detection of Radio Signals in Telecommunication Networks with Noises. Proceedings of the 1st International Workshop on Computer Information Technologies in Industry 4.0 (CITI 2023). CEUR Workshop Proceedings. Ternopil, Ukraine, June 14-16, 2023. P.173-180. ISSN 1613-0073. [31] Palianytsia Yu. B. Suchasni pidkhody do opratsiuvannia fonokardiosyhnalu ta matematychna model yoho u vyhliadi periodychno korelovanoho vypadkovoho protsesu // Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky, 2016. Vyp. 2(235). S. 90–93. [in Ukrainian]. [32] Palaniza Y., Yavorska E., Shadrina H., Dediv L. (2018) Phonocardiosignal as a periodically correlated stochastic process preprocessing algorithm structure grounding. Scientific Journal of TNTU (Tern.), vol. 91, no 3, pp. 143-152. [33] Palaniza Y.B., Shadrina H.M., Khvostivskiy M.O., Dediv L.Ye., Dozorska O.F. Main theoretical basis of biosignals modeling. Znanstvena misel. Slovenia. 2018. №16. P. 39-44Wang, Xin, Tapani Ahonen, and Jari Nurmi. "Applying CDMA technique to network-on-chip." IEEE transactions on very large scale integration (VLSI) systems 15.10 (2007): 1091-1100. [34] Palaniza Y., Franchevska H. (2018) Enerhetychni aspekty obrobky biosyhnaliv u kardiolohichnii praktytsi [Energy aspects of biosignals processing in cardiology practice]. Book of abstract of the Ⅶ International scientific and technical conference of young researchers and students "Current issues in modern technologies" (Tern., 28-29 November 2018), vol. 3, pp. 243 [in Ukrainian]. [35] Osukhivska H. M. Matematychna model tonovoho syhnalu dlia diahnostyky stanu klapaniv sertsia liudyny: avtoref. dys. na zdobuttia nauk, stupenia kand. tekhn. nauk: 01.05.02 / H.M. Osukhivska. Ternopil, 1999. 20 p. [in Ukrainian]. [36] H. Osuhivs'ka and I. Kyslak, "Random processes statistic application for cardiosignals characteristics determination," MMET '96. VIth International Conference on Mathematical Methods in Electromagnetic Theory. Proceedings, Lviv, Ukraine, 1996, pp. 264-266, doi: 10.1109/MMET.1996.565708. [37] Osukhivska H. M. Matematychna model porodzhennia tonovoho syhnalu u vyhliadi relaksatsiinoho multypulsatora. Materialy 6-oi nauk. konf. TDTU imeni Ivana Puliuia. Ternopil: TDTU. 2002. P.9. [in Ukrainian]. [38] Khvostivska L., Khvostivskyy M., Dunetc V., Dediv I. Mathematical and Algorithmic Support of Detection Useful Radiosignals in Telecommunication Networks. Proceedings of the 2nd International Workshop on Information Technologies: Theoretical and Applied Problems (ITTAP 2022). Ternopil, Ukraine, November 22-24, 2022. P.314-318. ISSN 1613-0073. [39] I. V. Lytvynenko; P. O. Maruschak; S. A. Lupenko; Yu. I. Hats; A. Menou; S. V. 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Тип вмісту:	Conference Abstract
Розташовується у зібраннях:	Наукові публікації працівників кафедри біотехнічних систем

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