10.14489/td.2019.08.pp.028-034

2019, 08 August

DOI: 10.14489/td.2019.08.pp.028-034

Goriunov O. V., Slovtsov S. V.
APPLICATION OF KOTELNIKOV’S THEOREM TO ANALYSIS OF RANDOM PROCESSES
(pp. 28-34)

Abstract. Analysis of many dynamic tasks arising in engineering applications is associated with the construction of spectral characteristics. However, the application of spectral analysis to random oscillations, which in most cases describe real processes (technical, technological, etc.), has a number of features and limitations associated, in particular, with the anconvergence of the Fourier transform. The substantiated metrological evaluation of the spectra associated with the reliability of the applied results is complicated by the absence of a rigorous mathematical model of a random process. The above remarks were solved on the basis of application of Kotelnikov's theorem at decomposition of a random process on known eigenfunctions. The obtained decomposition allowed us to obtain a number of results in the field of correlation and spectral analysis of random processes: the stability of the ACF and the relationship with the statistical characteristics of the implementation is proved, the orthogonal decomposition of the random process in the form of a continuous function is presented, which allows us to consider the evaluation and analyze the characteristics of the realizations without the use of a fast Fourier transform; the natural relationship between ACF and spectral density for a time-limited signal is shown, and the symmetric form of recording the signal spectrum is justified.

Keywords: vibration, spectral density, processing, decomposition of random signals, correlation.

+ - About the Authors Click to collapse

O. V. Goriunov (JSC ATOMPROEKT, Saint-Petersburg, Russia) E-mail: Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра.
S. V. Slovtsov (JSC NPO CKTI, Saint-Petersburg, Russia) E-mail: Данный адрес e-mail защищен от спам-ботов, Вам необходимо включить Javascript для его просмотра.

+ - References Click to collapse

1. Vilenkin S. Ya. (1979). Statistical processing of random function research results. Moscow: Energiya. [in Russian language]
2. Aksenov B. E., Afon'kin I. V., Evmenov V. P., Nechiporenko M. I. (1974). Fundamentals of probability theory. Part 2. Introduction to mathematical statistics. Leningrad. [in Russian language]
3. Dzhenkins G., Vatts D. (1971). Spectral analysis and its applications, (1). Moscow: Mir. [in Russian language]
4. Goryunov O. V, Slovtsov S. V. (2017). Features of the spectral density of vibrational displacement of pipelines of nuclear power plants. Problemy mashinostroeniya i avtomatizatsii, (4), pp. 132 – 137. [in Russian language]
5. Slovtsov S. V., Soldatov A. S., Sinil'schikov A. E. et al. (2017). Measurement of vibration parameters of SVB RU pipelines with RBMK-1000 at the first unit of Smolensk NPP. Kontrol'. Diagnostika, (8), pp. 44 – 50. [in Russian language] DOI: 10.14489/td.2017.08.pp.044-050
6. Goryunov O. V., Slovtsov S. V. (2017). Problems of substantiation of vibrational strength of pipelines of nuclear power plants. Saint Petersburg: Izdatel'stvo Politekhnicheskogo universiteta. [in Russian language]
7. Dobrynin S. A., Fel'dman M. S., Firsov G. I. (1987). Methods for automated study of machine vibration. Moscow: Mashinostroenie. [in Russian language]
8. Ponomarev V. M. (Ed.), Litvinov A. P. (1974). Fundamentals of automatic regulation and control: a handbook for non-electrical specialties of universities. Moscow: Vysshaya shkola. [in Russian language]
9. Baskakov S. I. (2000). Radio circuits and signals. 3rd ed. Moscow: Vysshaya shkola. [in Russian language]
10. Tihonov V. I., Mironov M. A. (1977). Markov processes. Moscow: Sovetskoe radio. [in Russian language]
11. Bom D. (1965). Quantum theory. Moscow: Nauka. [in Russian language]
12. Bochner S. (1959). Lectures on Fourier integrals. New Jersey.
13. Mandel' L., Vol'f E. (2000). Optical coherence and quantum optics. Moscow: Fizmatlit. [in Russian language]
14. Hinchin A. Ya. (1938). Correlation theory of stationary stochastic processes. UMN, (5), pp. 42 – 51. [in Russian language]

+ - Purchase digital version of a single article Click to collapse

This article is available in electronic format (PDF).

The cost of a single article is 350 rubles. (including VAT 18%). After you place an order within a few days, you will receive following documents to your specified e-mail: account on payment and receipt to pay in the bank.

After depositing your payment on our bank account we send you file of the article by e-mail.

To order articles please copy the article doi:

10.14489/td.2019.08.pp.028-034

and fill out the form