Skip to main content
SpringerLink
Log in

Analysis of Estimation Error of Skewness and Kurtosis of Bunimovich-Rice Processes with Exponentially Power Waveform of Pulses

  • Published:
Radioelectronics and Communications Systems Aims and scope Submit manuscript

Abstract

Mathematical expectations and variances of estimates of skewness and kurtosis coefficients of the noise signal model have been derived in this study. The specified noise signals represent the Bunimovich–Rice processes with exponentially power waveform of pulses expressed in terms of cumulant coefficients of the specified processes. It is shown that the distribution of instantaneous values of Bunimovich–Rice processes is quite different from the Gaussian distribution. The root-mean-square and relative estimation errors of skewness and kurtosis coefficients depending on of the time constant and waveform parameter of elementary pulses, as well as distributions of pulse amplitudes (degenerate and gamma distributions) and their intensities are analyzed. Expressions for finding the minimal sample volumes are obtained that ensure the specified values of relative errors in estimating the skewness and kurtosis coefficients of Bunimovich–Rice processes. The minimal sample volumes depending on parameters of these processes have been determined that ensure the relative estimation errors, which do not exceed 1%.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

References

  1. M. J. Buckingham, Noise in Electronic Devices and Systems (Halsted Press, Sydney, 1983). URI: https://www.amazon.com/Electronic-Devices-electrical-electronic-engineering/dp/0853122180.

    Google Scholar 

  2. G. P. Zhigal’skii, Fluctuations and Noises in Electronic Solid-State Devices (Fizmatlit, Moscow, 2012).

    Google Scholar 

  3. M. Mihaila, D. Ursutiu, I. Sandu, "Electron-phonon coupling as the source of 1/f noise in carbon soot," Sci. Reports, v.9, n.1, p.947 (2019). DOI: https://doi.org/10.1038/s41598-018-36544-4.

    Article  Google Scholar 

  4. A. V. Yakimov, A. V. Klyuev, M. A. Krevskii, "The nature of introduced phase 1/f noise in microwave oscillators," J. Commun. Technol. Electron., v.65, n.1, p.84 (2020). DOI: https://doi.org/10.1134/S1064226920010076.

    Article  Google Scholar 

  5. T. S. Mohammed, M. Rasheed, M. Al-Ani, Q. Al-Shayea, F. Alnaimi, "Fault diagnosis of rotating machine based on audio signal recognition system: an efficient approach," Int. J. Simul. Syst. Sci. Technol. (2020). DOI: https://doi.org/10.5013/IJSSST.a.21.01.08.

    Article  Google Scholar 

  6. D. Wotzka, "Mathematical model and regression analysis of acoustic emission signals generated by partial discharges," Appl. Comput. Math., v.3, n.5, p.225 (2014). DOI: https://doi.org/10.11648/j.acm.20140305.15.

    Article  Google Scholar 

  7. S. I. Builo, "Physico-mechanical, chemical and statistical aspects of acoustic emission," Izv. Altai State Univ., n.1, p.11 (2019). DOI: https://doi.org/10.14258/izvasu(2019)1-01.

    Article  Google Scholar 

  8. D. Wittekind, M. Schuster, "Propeller cavitation noise and background noise in the sea," Ocean Eng., v.120, p.116 (2016). DOI: https://doi.org/10.1016/j.oceaneng.2015.12.060.

    Article  Google Scholar 

  9. V. P. Bakalov, Fundamentals of Biotelemetry (Radio i Svyaz’, Moscow, 2001).

    Google Scholar 

  10. R. M. Rangayyan, Biomedical Signal Analysis (John Wiley & Sons, Inc., Hoboken, NJ, USA, 2015). DOI: https://doi.org/10.1002/9781119068129.

    Book  Google Scholar 

  11. A. Karagiannis, P. Constantinou, "Noise components identification in biomedical signals based on Empirical Mode Decomposition," in 2009 9th International Conference on Information Technology and Applications in Biomedicine (IEEE, Washington, 2009). DOI: https://doi.org/10.1109/ITAB.2009.5394300.

    Chapter  Google Scholar 

  12. V. I. Bunimovich, Fluctuation Processes in Radioreceaving Devices (Sov. Radio, Moscow, 1951).

    Google Scholar 

  13. S. O. Rice, "Mathematical Analysis of Random Noise," Bell Syst. Tech. J., v.23, n.3, p.282 (1944). DOI: https://doi.org/10.1002/j.1538-7305.1944.tb00874.x.

    Article  MathSciNet  MATH  Google Scholar 

  14. V. I. Tikhonov, Statistical Radio Engineering (Radio i Svyaz’, Moscow, 1982).

    Google Scholar 

  15. B. R. Levin, Theoretical Foundations of Statistical Radio Engineering (Radio i Svyaz’, Moscow, 1989).

    MATH  Google Scholar 

  16. A. N. Malakhov, Cumulant Analysis of Random Non-Gaussian Processes and their Transformations (Sov. Radio, Moscow, 1978).

    MATH  Google Scholar 

  17. A. I. Krasilnikov, V. S. Beregun, T. A. Polobyuk, Cumulant Methods in Problems of Noise Diagnostics of Heat-Power Equipment (Osvita Ukrainy, Kyiv, 2019).

    Google Scholar 

  18. D. Alexandrou, C. de Moustier, G. Haralabus, "Evaluation and verification of bottom acoustic reverberation statistics predicted by the point scattering model," J. Acoust. Soc. Am., v.91, n.3, p.1403 (1992). DOI: https://doi.org/10.1121/1.402471.

    Article  Google Scholar 

  19. H. Wang, P. Chen, "Fault diagnosis method based on kurtosis wave and information divergence for rolling element bearings," WSEAS Trans. Syst., v.8, n.10, p.1155 (2009).

    Google Scholar 

  20. V. V. Kuznetsov, "Use of the Third Order Moments in Electric Load Calculations," Vestn. Samar. GTU. Seriya Tekhnicheskie Nauk., v.24, n.2, p.166 (2009).

    Google Scholar 

  21. A. I. Krasil’nikov, V. S. Beregun, "Application of the orthogonal representation method for determining the probability densities of typical models of fluctuation signals," Radioelectron. Commun. Syst., v.54, n.11, p.592 (2011). DOI: https://doi.org/10.3103/S0735272711110021.

    Article  Google Scholar 

  22. B. F. Kuznetsov, D. K. Borodkin, L. V. Lebedeva, "Cumulant MODELS OF COMPLEMENTARY ERRORS," Mod. Technol. Syst. Anal. Model., n.1, p.134 (2013).

    Google Scholar 

  23. V. Palahin, J. Juhár, "Joint Signal Parameter Estimation in Non–Gaussian Noise by the Method of Polynomial Maximization," J. Electr. Eng., v.67, n.3, p.217 (2016). DOI: https://doi.org/10.1515/jee-2016-0031.

    Article  Google Scholar 

  24. V. S. Beregun, A. I. Krasilnikov, "Research of excess kurtosis sensitiveness of diagnostic signals for control of the condition of the electrotechnical equipment," Tech. Electrodyn., v.2017, n.4, p.79 (2017).

    Google Scholar 

  25. S. W. Zabolotnii, S. S. Martynenko, S. V. Salypa, "Method of Verification of Hypothesis about Mean Value on a Basis of Expansion in a Space with Generating Element," Radioelectron. Commun. Syst., v.61, n.5, p.222 (2018). DOI: https://doi.org/10.3103/S0735272718050060.

    Article  Google Scholar 

  26. I. P. Shumeiko, M. I. Ozhiganova, "Modelling of the sea surface from description of radar altimeter return waveform," J. Radio Electron., v.2018, n.12, p.1 (2018). DOI: https://doi.org/10.30898/1684-1719.2018.12.12.

    Article  Google Scholar 

  27. A. Krasilnikov, V. Beregun, O. Harmash, "Analysis of Estimation Errors of the Fifth and Sixth Order Cumulants," in 2019 IEEE 39th International Conference on Electronics and Nanotechnology (ELNANO) (IEEE, Washington, 2019). DOI: https://doi.org/10.1109/ELNANO.2019.8783910.

    Chapter  Google Scholar 

  28. G. McLachlan, D. Peel, Finite Mixture Models (John Wiley & Sons, Inc., Hoboken, NJ, 2000). DOI: https://doi.org/10.1002/0471721182.

    Book  MATH  Google Scholar 

  29. H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, NJ, 1999).

    MATH  Google Scholar 

  30. A. Stuart, J. K. Ord, Kendall’s Advanced Theory of Statistics, Volume 1: Distribution Theory (Wiley, New Jersey, 2010). URI: https://www.wiley.com/en-us/Kendall%27s+Advanced+Theory+of+Statistics%2C+Volume+1%2C+Distribution+Theory%2C+6th+Edition-p-9780470665305.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine

    A. I. Krasil’nikov

  2. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    V. S. Beregun

Authors
  1. A. I. Krasil’nikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. S. Beregun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. S. Beregun.

Ethics declarations

ADDITIONAL INFORMATION

A. I. Krasil’nikov and V. S. Beregun

The authors declare that they have no conflict of interest.

The initial version of this paper in Russian is published in the journal “Izvestiya Vysshikh Uchebnykh Zavedenii. Radioelektronika,” ISSN 2307-6011 (Online), ISSN 0021-3470 (Print) on the link http://radio.kpi.ua/article/view/S0021347020080051 with DOI: https://doi.org/10.20535/S0021347020080051

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krasil’nikov, A.I., Beregun, V.S. Analysis of Estimation Error of Skewness and Kurtosis of Bunimovich-Rice Processes with Exponentially Power Waveform of Pulses. Radioelectron.Commun.Syst. 63, 430–440 (2020). https://doi.org/10.3103/S0735272720080051

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0735272720080051

Search

Navigation