Скользящая пространственно-частотная обработка финитных двумерных действительных дискретных сигналов на основе преобразования Фурье с варьируемыми параметрами

A V Ponomarev; O V Ponomareva

doi:10.22213/2410-9304-2021-4-138-147

Authors

A. V. Ponomarev Kalashnikov ISTU
O. V. Ponomareva Kalashnikov ISTU

DOI:

https://doi.org/10.22213/2410-9304-2021-4-138-147

Keywords:

two-dimensional discrete finite signal, direct two-dimensional discrete Fourier transform with variable parameters, reference domain, spatial frequency spectrum, sliding processing

Abstract

In the field of Fourier processing of finite signals, three main directions of scientific research have been identified: Fourier processing of one-dimensional finite signals - processing of scalar functions of a scalar argument, Fourier processing of two-dimensional finite signals - processing of scalar functions of a vector argument, multichannel Fourier processing - processing of vector functions of a scalar argument. As part of the creation of a generalized theory of Fourier processing of finite signals, the authors proposed: the theory of spectral analysis of discrete signals at finite intervals in the bases of parametric exponential functions and the theory of two-dimensional digital signal processing in Fourier bases with variable parameters. The developed theories, generalizing the theory of Fourier processing of one-dimensional and two-dimensional signals, are based: on the introduction of new concepts of the shift of finite discrete signals in one-dimensional and two-dimensional cases and the introduction of new basic Fourier processing systems of discrete signals, which have the properties of multiplicativity, functions in the system. The mathematical apparatus of two-dimensional discrete Fourier transform with variable parameters in matrix and algebraic form is considered. A new method for processing finite two-dimensional real discrete signals in the spatial-frequency domain based on the discrete Fourier transform with variable parameters, the method of sliding spatial-frequency processing, has been introduced. An efficient method and algorithm for fast diagonal sliding spatial-frequency processing of finite two-dimensional real discrete signals based on the discrete Fourier transform with variable parameters has been developed. The estimation of the efficiency and effectiveness of the algorithm of the diagonal sliding two-dimensional discrete Fourier transform with variable parameters from the point of view of computational costs is carried out. As a result of experimental studies on model two-dimensional discrete finite signals, the validity, efficiency and reliability of the proposed method of sliding spatial-frequency processing of finite two-dimensional real discrete signals based on the discrete Fourier transform with variable parameters have been proved. A comparison (from the point of view of computational costs) of the developed method of sliding spatial-frequency processing of finite two-dimensional real discrete signals based on the discrete Fourier transform with variable parameters with the standard method of sliding processing of this type of signals is carried out.

Author Biographies

A. V. Ponomarev, Kalashnikov ISTU

PhD in Economics

O. V. Ponomareva, Kalashnikov ISTU

DSc in Engineering, Professor

References

Rabiner L., Gold B. Theory and Application of digital signal processing. New Jersey, Prentice-hall, 1975, 772 p.

Favorskaya M., Savchina E., Popov A. Adaptive visible image watermarking based on Hadamard transform. IOP Conference Series: Materials Science and Engineering, 2018, vol. 450, no. 5, MIST Aerospace, pp. 052003.1-052003.6. doi: 10.1088/1757-899X/450/5/ 052003

Klionskiy D. M., Kaplun D. I., Geppener V. V. Empirical more decomposition for signal preprocessing and classification of intrinsic mode functions. Pattern Recognition and Image Analysis (Advances in Mathematical Theory and Applications). 2018. Vol. 28. No. 1. Pp. 122-132. Doi:10.1134/S1054661818010091.

Ponomarev A.V., Ponomareva O.V. Digital technologies in non-destructif testing. In: Journal of Physics: Conference Series. 2019. С. 12038.

Ponomareva O.V., Ponomarev A.V. Application of parametric discret Fourier transform non-destructif testing of composite materiaials with a free oscilation metod In: Journal of Physics: Conference Series. 2019. С. 12039.

Batishchev V. I.,Volkov I. I., Zolin A. G. Using a stochastic basis in signal and image recovery problems. Optoelectronics, Instrumentation and Data Processing, 2017. Vol. 53. No. 4. Pp. 414-420.

Kulikovskikh I., Prokhorov S. Psychological perspectives on implicit regularization: a model of retrieval-induced forgetting (RIF). In: Journal of Physics: Conference Series. electronic edition, 2018. Pp. 012079. Doi:10.1088/1742-6596/1096/1/012079

Favorskaya M. N., Buryachenko V. V. Authentication and copyright protection of videos under transmitting specifications. In: Computer Vision in Advanced Control Systems-5. ISRL. Favorskaya M. N., Jain L. C. (eds). Springer, Cham, 2020. Vol. 175. Pp. 119-160. doi.org/10.1007/978-3-030-33795-7_5.

Blahut, R. E., Fast Algorithms for Digital Signal Processing. Reading, MA: Addison-Wesley, 1984.

Petrovsky N. A., Rybenkov E. V., Petrovsky A. A. In: Signal Processing - Algorithms, Architectures, Arrangements, and Applications Conference Proceedings, SPA. 22. Сер. "SPA 2018 - Signal Processing: Algorithms, Architectures, Arrangements, and Applications, Conference Proceedings", 2018, pp. 120-125. Doi: 10.23919/SPA.2018.8563311

Likhttsinder B. Conditional average value of queues in queuing systems with bath request flows. In: 2017 4th International Scientific-Practical Conference Problems of Infocommunications Science and Technology, PIC S and T 2017 - Proceedings. 2018, pp. 49-52. Doi:10.1109/INFOCOMMST.2017.8246347.

Bakulin M.G., Vityazev V.V., Shumov A.P., Kreyndelin V.B. Effective signal detection for the spatial multiplexing mimo systems. Telecommunications and Radio Engineering, 2018. vol. 77, no. 13, pp. 1141-1158. doi.org/10.1615/TelecomRadEng.v77.i13.30.

Prozorov D., Tatarinova A. Comparison of grapheme-to-phoneme conversions for spoken document In: 2019 IEEE East-West Design and Test Symposium, EWDTS 2019, 2019, pp. 8884449. doi:10.1109/ EWDTS.2019.8884449.

Prozorov D., Trubin I. Detection of a signal in the simo system with spatial correlation of noise. In: 2018 7th Mediterranean Conference on Embedded Computing, MECO 2018 - Including ECYPS 2018, Proceedings. 7. 2018, pp. 1-5. doi:10.1109/MECO.2018.8405965.

Urakov A., Gurevich K., Alies M., Reshetnikov A., Kasatkin A., Urakova N. The tissue temperature during injection of drug solution into it as an integral indicator of rheology. In: Journal of Physics: Conference Series. 4th International Conference on Rheology and Modeling of Materials, IC-RMM 2019, 2020, pp. 012003. Doi:10.1088/1742-6596/1527/1/012003.

Gonzalez R.C., Woods R.E. Digital Image Processing, 4th Ed. Published by Pearson. 2018.-1168 pages.

Pratt William K. Digital image processing. 4th edl, A Wiley-Interscience publication 2007, 807 p.

Rabiner L., Gold B. Theory and Application of digital signal processing. New Jersey, Prentice-hall, 1975, 772 p.

Пономарев А. В. Основы теории двумерной цифровой обработки сигналов в базисах Фурье с варьируемыми параметрами // Цифровая обработка сигналов. 2019. № 2. С. 12-20.

Пономарева О. В., Пономарев А. В. Интерполяция в пространственной области двумерных дискретных сигналов с помощью быстрых преобразований Фурье // Интеллектуальные системы в производстве. 2019. Т. 17, № 1. С. 88-94. DOI 10.22213/24-10-9304-2019-1-88-94.

Пономарева О. В., Пономарев А. В., Смирнова Н. В. Цифровизация измерений спектров в базисе Фурье - тенденции развития и проблемы // Приборы и методы измерений. 2019. Т. 10. № 3. С. 271-280. DOI 10.21122/2220-9506-2019-10-3-271-280.

Dzhenkins G., Vatts D. Spektral'nyj analiz i ego prilozheniya: Vyp.1 Per s angl. V.F.Pisarenko [Spectral analysis and its applications: Vol.1 Per from English. VF Pisarenko]. Moscov, Mir, 1971, 312 p. (in Russ.).

Dzhenkins G., Vatts D. Spektral'nyj analiz i ego prilozheniya: Vyp.1 Per s angl. V.F.Pisarenko [Spectral analysis and its applications: Vol.2 Per from English. VF Pisarenko]. Moscov, Mir, 1971, 287 p. (in Russ.).

Milent'ev V.S., Batishchev V.I. Approksimacionnye metody i sistemy izmereniya i kontrolya parametrov periodicheskih signalov [Approximation methods and systems for measuring and monitoring parameters of periodic signals.]. Moscov, Fizmatlit, 2011, 240 p. (in Russ.).

Bendat Dzh., Pirsol A. Prikladnoj analiz sluchajnyh processov: Per. s angl.[ Applied analysis of random processes: Trans. from English]. Moscov, Mir, 1989, 540 p. (in Russ.).

Marpl-ml. S.L. Cifrovoj spektral'nyj analiz i ego prilozheniya: Perevod s angl. [Digital Spectral Analysis and its Applications]. Moscow, World., 1990, 584 p. (in Russ.).

Oppengejm EH. Primenenie cifrovoj obrabotki signalov: Perev. s angl. [The use of digital signal processing: Trans. from English]. Moscow, Mir,1980. 552 p. (in Russ.).

Yaglom A.M. Korrelyacionnaya teoriya stacionarnyh sluchajnyh funkcij s primerami iz meteorologii [Correlation theory of stationary random functions with examples from meteorology].Leningrad, 1981, 281 p. (in Russ.).

Batishchev V.I., Zolin A.G.,Kosarev D.N., Romaneev A.E. [Approximation approach to solving the problems of analyzing and interpreting experimental data]. Herald of Samara State University. Series: Engineering, 2006, no. 40, pp. 57-65 (in Russ.).

Batishchev V.I., Melent'ev V.S. [Measuring and modeling approach to determining the integral characteristics of periodic signals] News of higher educational institutions. Electromechanics, 2003, no.6, pp.36-39 (in Russ.).

Batishchev V.I., Volkov I.I., Zolin A.G. [The use of the stochastic basis in the problems of the restoration of signals and images]. Avtometriya, 2017, vol. 53, no.4, pp.127-134 (in Russ.).

Batishchev V.I., Volkov I.I., Zolin A.G. [The study of the approximation properties of functional bases in the tasks of image reconstruction during remote sensing of the earth].In the collection: Control and modeling problems in complex systems, works of the XVIII International Conference. Edited by: E.A. Fedosova, N.A. Kuznetsova, V.A. Wittych, 2016, pp. 304-307 (in Russ.).

Prokhorov S.A., Kulikovskikh I.M. Unique Condition for generalized Laguerre Functions to solve pole Position Problem, Signal Processing, 2015. Vol. 108. Pp. 25-29.

Prohorov S.A., Grafkin V.V. Strukturno-spektral'nyj analiz sluchajnyh processov [Structural and spectral analysis of random processes]. Samara, 2010.

Prozorov D.E., Petrov E.P. Bystryj poisk shumopodobnyh signalov. Edited by: E.P.Petrova [Quick search for noise-like signals]. Kirov, 2006.

Пономарева О. В. Развитие теории и разработка методов и алгоритмов цифровой обработки информационных сигналов в параметрических базисах Фурье : дис. … д-ра техн. наук: 05.13.01. Ижевск, 2016. 357 с.