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2. Farhang-Boroujeny B. A square-root Nyquist (M) filter design for digital communication systems// IEEE Trans on SP, 2008, vol. 56, no. 5, pp. 2127-2132. 3. Ashrafi A. Optimized linear phase square-root Nyquist FIR filters for CDMA IS-95 and UMTS standards// Signal Processing, 2013, vol. 93, no. 4, pp. 866-873. 4. Traverso S. A family of square-root Nyquist filter with low group delay and high stopband attenuation// IEEE Commun. Letters, 2016, vol. 20, no. 6, pp. 1136-1139. 5. Xiao R., Lei Q., Guo X., Du W., Zhao Y. A design of two sub-stage square-root Nyquist matched filter// IEEE Access, 2018, vol. 6, may, pp. 23292-23302. 6. Mingazin A. T. Design quantized pulse-shaping FIR filters for digital communication system// Digital Signal processing. Russian Scientific and Technical Journal, 2021, no. 4, pp. 3-15. 7. Mingazin A. T. Weighted Chebyshev approximation in design of pulse-shaping FIR filters for digital communication system// Digital Signal processing. Russian Scientific and Technical Journal, 2022, no. 2, pp. 3-11.
It is shown that for nonlinear filters, the range of the adaptation parameters of gradient algorithms narrows compared to the linear case and is determined by high-order correlation moments. To speed up the convergence rate of gradient adaptation algorithms for processes with a symmetric probability distribution density, instead of carrying out a time-consuming orthogonalization operation, an algorithm based on separate adaptation of even and odd nonlinear components of the filter is proposed. This approach is considered using the example of a third-order nonlinear filter, for which estimates of the permissible limits of the adaptation parameters were obtained. In order to equalize the rate of convergence of individual nonlinear components of the filter, a sequential adaptation algorithm is proposed, based on performing iterations in the direction of increasing the order of nonlinearity of the filter components. The convergence of such an algorithm is proven and estimates for the choice of its parameters are obtained. It is shown that, along with increasing the speed of convergence, the sequential adaptation algorithm at the same time does not guarantee convergence to the optimal point. To achieve the required accuracy without a significant loss of adaptation speed, a combined scheme is proposed, based on the joint use of sequential and parallel adaptation algorithms, using the latter to refine the current vector of filter coefficients. Another possible solution is to add additional feedback to the sequential circuit, the periodic closure of which leads to a decrease in the systematic adaptation error. Increasing and leveling the speed of convergence of the adaptation process can be achieved through the use of Newton-type algorithms (recursive least squares algorithms). A recursive algorithm for adapting polynomial filters with exponential weighting is proposed, which, along with increasing the convergence rate, ensures smoothing of random fluctuations when approaching the optimal point, as well as equalization of the convergence rate relative to the nonlinear components of the filter. 2. Widrow B., uel D. Stearns S. D. Adaptive signal processing. Prentice-Hall, 1985. 474 p. 3. Haykin S. Adaptive filter theory. NJ: Prentice-Hall, 1991. 936 p. 4. Dzhigan V.I. Adaptive signal filtering: theory and algorithms. M.: Tekhnosphere, 2013. 528 p. 5. Doyle III F.J., Pearson R.K., Ogunnaike B.A. Identification and control using Volterra models. London: Springer-Verlag, 2002. 318 p. 6. Hansler E., Schmidt G. Acoustic echo and noise control: A practical approach. Hoboken, NJ: Wiley, 2004. 472 p. 7. Menshikov B.N., Priorov A.L. Nonlinear echo compensation based on an adaptive polynomial Volterra filter with a dynamically tunable structure // Digital signal processing. 2006. No. 3. P. 20-25. 8. Stepanov O.A., Neural network algorithms in the problem of nonlinear estimation. Interrelation with the Bayesian approach // Navigation and motion control: materials of reports of the XI conference of young scientists. 2009. pp. 39-65. 9. Mitra S. K., Sicuranza G. L. Nonlinear image processing. Academic Press, 2001. 455 p. 10. Mathews V. J., Sicuranza G. L. Polynomial signal processing. New York: John Wiley & Songs Interscience publication, 2000. 472 p. 11. Shcherbakov M.A., Steshenko V.B., Gubanov D.A. Digital polynomial filtering in real time: algorithms and implementation methods on a modern element base // Digital signal processing. 2000. No. 1. P. 19-26. 12. Mathews V. J. Adaptive polynomial filters // IEEE Signal Processing Magazine. 1991. No. 7. P. 10-26. 13. Pupkov K.A., Kapalin V.I., Yushchenko A.S. Functional series in the theory of nonlinear systems.. M.: Nauka. 1976. 448 p. 14. Shcherbakov M. A. A Recursive Algorithm of Digital Polynomial Filtering. 2020 Moscow Workshop on Electronic and Networking Technologies (MWENT), March 11-13, 2020, Moscow, Russia, 4 pages. DOI: 10.1109/MWENT47943.2020.9067458. 15. Shcherbakov M.A. Construction of optimal nonlinear filters by the method of successive approximations // Analytical mechanics, stability and control: Proceedings of the X International Chetaev Conference. T. 3. Section 3. Control. Part II. Kazan, June 12-16, 2012 – Kazan: Kazan Publishing House. State Tech. Univ., 2012. P. 472-482. 16. Lancaster P. Theory of matrices. M.: Nauka, 1978. 280 p. 17. Pottmann M. Application of general multi-model approach for identification of highly nonlinear processes – a case study / M. Pottmann, H. Unbehauen, D.E. Seborg // Int. Journal of Control. 1993. V. 57. No. 1. P. 97-120. 18. Marmarelis V. Marmarelis M. Analysis of physiological systems. The White-Noise Approach. New York: Plenum Press. 1978. 488 p.
The aim of the work is to optimize the weight coefficients of non–recursive rejection filters depending on the correlation properties of passive interference according to the probability criterion. Expressions are obtained for the probabilistic characteristics of detection systems with coherent interference rejection and subsequent coherent or non-coherent accumulation of rejection residues, respectively. These expressions establish a functional relationship between the probability of correct detection averaged over the Doppler phase of the signal and the correlation parameters of the passive interference and the characteristics of the detection system. The criteria for the optimization of the weight vector of the rejection filter are given. These criteria make it possible to establish the relationship of the optimal weight vector with the interference parameters based on nonlinear programming methods. A quasi-Newtonian iterative procedure for finding the optimal vector is given. In order to achieve a unimodal extremum, restrictions on the frequency response of the rejection filter are introduced. Numerical results of optimization of a system with coherent rejection and subsequent incoherent equilibrium accumulation according to a probabilistic criterion are considered. Their comparison with similar results of optimization of the rejection filter according to the energy criterion is carried out. The proposed method of optimization of detection systems by probabilistic criterion makes it possible to obtain significant gains in the efficiency of signal detection compared to optimization by energy criterion and to realize the marginal efficiency for the class of systems under consideration. 2. Richards M.A., Scheer J.A., Holm W.A. (Eds.). Principles of Modern Radar: Basic Principles. New York: SciTech Publishing, IET, Edison. 2010. – 924 p. 3. Melvin W. L., Scheer J.A. (Eds.). Principles of Modern Radar: Advanced Techniques. New York: SciTech Publishing, IET, Edison, 2013. – 846 p. 4. Radar Handbook / Ed. by M.I. Skolnik. 3rd ed. McGraw–Hill, 2008. 1352 p. 5. Popov D.I. Adaptacija nerekursivnyh rezhektornyh fil'trov // Izvestija vuzov. Ra-diojelektronika. 2009. vol. 52. no. 4. P. 46-55. (in Russian). 6. Popov D.I. Autocompensation of the Doppler phase of clutter // Cifrovaja obrabotka signalov. 2009. no 2. pp. 30–33. (in Russian). 7. Popov D.I. Avtokompensacija doplerovskoj fazy mnogochastotnyh passivnyh pomeh // Vestnik Rjazanskogo gosudarstvennogo radiotehnicheskogo universiteta. 2018. no. 65. pp. 32–37. 8. Popov D.I. Adaptive suppression of clutter // Cifrovaja obrabotka signalov. 2014. no. 4. pp. 32-37. (in Russian). 9. Popov D.I. Adaptivnije regektornjie filtrij kaskadnogo tipa // Cifrovaya obrabotka signalov. 2016. no. 2. pp. 53-56. (in Russian). 10. Popov D.I. Adaptive notch filter with real weights // Cifrovaya obrabotka signalov. 2017. no. 1. pp. 22-26. (in Russian). 11. Popov D.I. Optimizacja nerekursivnjih regektornjie filtrov s chastichnoj adaptaciej // Cifrovaya obrabotka signalov. 2018. no. 1. pp. 28-32. (in Russian). 12. Popov D.I. Optimizacija rezhektornyh fil'trov po verojatnostnomu kriteriju // Cifrovaja obrabotka signalov. 2021. no. 1. P. 55-58. (in Russian). 13. Kuz'min S.Z. Cifrovaja radiolokacija. Vvedenie v teoriju (Digital radar. Introduction to Theory). Kiev: KViC, 2000. 428 p. (in Russian). 14. Cifrovaja obrabotka signalov v mnogofunkcional'nyh radiolokatorah. Metody. Algoritmy. Apparatura: monografija (Digital signal processing in multifunctional radars. Methods. Algorithms. Equipment: monograph) / pod red. G.V. Zajceva. M.: Radiotehnika, 2015. 376 p. (in Russian). 15. Klochko V.K., Kuznecov V.P., Levitin A.V. i dr. Algoritmy opredelenija koordi-nat dvizhushhihsja celej na baze mnogokanal'noj doplerovskoj RLS // Vestnik Rjazanskogo gosudarstvennogo radiotehnicheskogo universiteta. 2015. no. 53. pp. 3-10. (in Russian). 16. Klochko V.K., Kuznecov V.P., Vu Ba Hung. Ocenivanie parametrov radiosignalov ot podvizhnyh malovysotnyh ob#ektov // Vestnik Rjazanskogo gosudarstvennogo radioteh-nicheskogo universiteta. 2022. no. ¹ 80. pp. 12-23. (in Russian). 17. Popov D.I., Belokrylov A.G. Sintez obnaruzhitelej-izmeritelej mnogochastotnyh signalov // Izvestija vuzov. Radiojelektronika. 2001. v. 44. no. 11. pp. 33-40. (in Russian). 18. Middlton D. Vvedenie v statisticheskuju teoriju svjazi (Introduction to the statistical theory of communication): v 2 t. per. s angl. M.: Sov. Radio, 1961. v. 1. 782 p.; 1962. v. 2. 832 p. (in Russian).
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V.K. Klochko, e-mail: klochkovk@mail.ru B. H. Vu, e-mail: ronando2441996@gmail.com Ryazan State Radio Engineering University, Russia, Ryazan Keywords:
2. K. Ghartey , A. Papandreou-Suppappola , and D. Cochran , On the Use of Matching Pursuit Time-Frequency Techniques for Multiple-Channel Detection, in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, 5, 3201–3204, May 2001. 3. Papandreou-Suppappola, Antonia, Applications in time-frequency signal processing (Electrical engineering and applied signal processing series), New York, 2002, 397 ð. 4. Klochko V. K., Vu B. H. Time-frequency signal processing in Doppler radios // Digital signal processing. 2023. No. 2. pp. 15-21. 5. Klochko V. K., Kuznetsov V. P., Vu B. H. Estimation of parameters of radio signals from mobile low-altitude objects // Bulletin of the Ryazan State Radio Engineering University. 2022. Issue 80. pp. 12-23. 6. Bakulev P. A. Radar systems. Textbook for universities. 3rd edition, revised. and additional M.: Radio Engineering, 2015. 440 p. 7. Klochko V. K., Vu B. H.. Detection of mobile sources by a radio receiver system // Digital signal processing. 2022. ¹ 4. Pp. 50-55.
The article analyzes video information path in aerospace hyperspectral imaging systems of Earth and describes ways to usage this knowledge for improve neural network object identification performance. The video information path is represented as multiply of two functions, one of which depends only on solar radiation wavelength, and the other on coordinates of scanned point and solar radiation wavelength. Based on video information path representation some important practical tasks were generated: 1) estimation of spectral reflectance coefficient; 2) clarification of atmospheric transmission coefficients; 3) clarification of parameters of video information path during flight of satellite. This study focuses on solving the first task. An analyze of radiometric quality of the hyperspectral sensor was performed. The issue of reducing the redundancy of hyperspectral output data for neural network processing is considered. For experimental research, data from the aviation system «AVIRIS» and the Russian space system «Resurs-P» are used. Some experiments are presented for demonstrating the effect of reducing data redundancy with principle component method. Quality metrics of neural network object identification were obtained. 2. H. Kaufmann et al., "EnMAP A Hyperspectral Sensor for Environmental Mapping and Analysis," 2006 IEEE International Symposium on Geoscience and Remote Sensing, Denver, CO, USA, 2006, pp. 1617-1619. 3. Akhmetianov V. R.. Nikolenko A. A.. Terentyeva V. V. Razvitiye kosmicheskoy giperspektralnoy apparatury za rubezhom // mater. nauch.-tekhn. konf. «Giperspektralnyye pribory i tekhnologii». M.: OAO «Krasnogorskiy zavod im. S.A.Zvereva». 2013. pp. 41-42. 4. Eremeev V.V.. Egoshkin N.A.. Makarenkov A.A.. Moskvitin A.E.. Ushenkin V.A. Problemnyye voprosy obrabotki dannykh ot kosmicheskikh sistem giperspektralnoy i radiolokatsionnoy syemki Zemli // Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2017. ¹60. pp. 54-64. 5. Arkhipov S. A.. Lyakhov A. Yu.. Tarasov A. P. Raboty OAO «Krasnogorskiy zavod im. S.A. Zvereva» po sozdaniyu giperspektralnykh priborov distantsionnogo zondirovaniya // mater. nauchn.-tekhn. konf. «Giperspektralnyye pribory i tekhnologii». M.: OAO «Krasnogorskiy zavod im. S.A. Zvereva». 2013. pp. 25-30. 6. Kirilin A. N.. Akhmetov R. N.. Stratilatov N. R.. Baklanov A. I.. Federov V. M.. Novikov M. V. Kosmicheskiy apparat «Resurs-P» // Geomatika. 2010. ¹ 4. pp. 23-26. 7. Antonushkina S. V.. Eremeev V. V.. Makarenkov A. A.. Moskvitin A. E. Osobennosti analiza i obrabotki informatsii ot sistem giperspektralnoy syemki Zemnoy poverkhnosti // Tsifrovaya obrabotka signalov. 2010. ¹ 4. pp. 38-43. 8. Akhmetov R.N.. Vezenov V.I.. Eremeev V.V.. Stratilatov N.R.. Yudakov A.A. Modeli formiro-vaniya i nekotoryye algoritmy obrabotki giperspektralnykh izobrazheniy // Issledovaniye Zemli iz kosmosa. 2014. ¹1. pp. 17-28. 9. Uspenskiy A. B.. Rublev A. N. Sovremennoye sostoyaniye i perspektivy sputnikovogo giperspektralnogo atmosfernogo zondirovaniya // Issledovaniye Zemli iz kosmosa. 2013. ¹ 6. pp. 4-15. 10. Grigoryeva O. V. Nablyudeniye degradatsii lesov po dannym giperspektralnogo aero- kosmicheskogo zondirovaniya // Issledovaniye Zemli iz kosmosa. 2014. ¹1. pp. 43-48. 11. Eremeev V.V.. Egoshkin N.A.. Makarenkov A.A.. Ushenkin V.A.. Postylyakov O.V. Uluchsheniye tekhnologiy iskusstvennogo intellekta pri obrabotke materialov nablyudeniya Zemli na osnove sistemnogo analiza skvoznogo informatsionnogo trakta // Sovremennyye problemy distantsionnogo zondirovaniya Zemli iz kosmosa. 2023. vol.20. ¹6. pp.144-154. 12. Eremeev V.A.. Makarenkov A.A. 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Muhammad Ahmad, Adil Mehmood Khan, Manuel Mazzara, Salvatore Distefano, Mohsin Ali, Muhammad Shahzad Sarfraz. A fast and compact 3-D CNN for hyperspectral image classification. IEEE Geoscience and Remote Sensing Letters. 2022. vol.19. pp. 1-5. 18. Marina Sokolova, Guy Lapalme. A systematic analysis of performance measures for classification tasks. Information Processing and Management. 2009. 45(4). pp. 427-437. 19. Schowengerdt R. A., Remote Sensing: Models and Methods for Image Processing, 3rd ed., San Diego, CA: Academic Press, 2006, 558 p.
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