Skip to main content
SpringerLink
Log in

Criterion of Significance Level for Selection of Order of Spectral Estimation of Entropy Maximum

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

Abstract

It is researched a wide class of parametric estimations of power spectral density based on principle of entropy maximum and autoregression observation model. At that there is distinguished the key parameter which is used model order. It is considered a problem of a priori uncertainty when true value of order is a priori unknown. It is proposed a new criterion for definition of order using finite sampling volume with purpose of overcome of the drawbacks of existing algorithms in conditions of small sampling. The principle of guaranteed significance level in a problem of complex statistic hypothesis verification is a basic principle of this criterion. In contrast to criteria of AIC, BIC, etc. this criterion is not related to determination of measurements inaccuracy, since it uses a conception of “significance level” of formed solution only. The efficiency of proposed criterion is researched theoretically and experimentally. An example of its application in a problem of spectral analysis of voice signals is considered. Recommendations about its practical application in the systems of digital signal processing are given.

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

Similar content being viewed by others

References

  1. S. M. Kay, Modern Spectral Estimation: Theory and Application (Prentice-Hall signal processing series, 1999).

    Google Scholar 

  2. L. R. Rabiner, R. W. Schafer, Theory and Applications of Digital Speech Processing (Pearson, Boston, 2010).

    Google Scholar 

  3. J. Gibson, “Entropy power, autoregressive models, and mutual information,” Entropy 20, No. 10, 750 (2018). DOI: 10.3390/e20100750.

    Article  Google Scholar 

  4. S. L. Marple Jr., Digital Spectral Analysis with Applications (Prentice-Hall, 1987).

    Google Scholar 

  5. F. Castanié (ed.), Digital Spectral Analysis: Parametric, Non-Parametric and Advanced Methods (Wiley-ISTE, 2011). URI: https://www.wiley.com/en-us/Digital+Spectral+Analysis%3A+Parametric%2C+Non+Parametric+and+Advanced+Methods-p-9781848212770 .

    MATH  Google Scholar 

  6. V. V. Savchenko, “The new concept of the software of statistical information processing on the basis of predictive function of probability theory,” Nauchnyye Vedomosti BelGU. Ser: Ekonomika. Informatiks 34/1, No. 7, 84 (2015). URI: http://dspace.bsu.edu.ru/handle/123456789/13130 .

    Google Scholar 

  7. C.-A. Liu, B.-S. Kuo, W.-J. Tsay, “Autoregressive spectral averaging estimator,” IEAS Working Paper: academic research 17-A013. Institute of Economics (Taiwan, 2017). URI: https://ideas.repec.org/p/sin/wpaper/17-a013.html .

    Google Scholar 

  8. E. O. Zaitsev, V. E. Sydorchuk, A. N. Shpilka, “Application of the spectrum analysis with using Berg method to developed special software tools for optical vibration diagnostics systems,” Devices Methods Meas. 7, No. 2, 186 (2016). DOI: 10.21122/2220-9506-2016-7-2-186-194.

    Article  Google Scholar 

  9. V. A. Kakora, A. V. Grinkevich, “Mathematical analysis of spectral estimation algorithms resolution,” Doklady BGUIR, No. 3, 20 (2017). URI: https://elibrary.ru/item.asp?id=29855484 .

    Google Scholar 

  10. MATLAB Examples. URI: https://www.mathworks.com/examples/signal/category/spectral-analysis .

  11. J. Ding, V. Tarokh, Y. Yang, “Bridging AIC and BIC: a new criterion for autoregression,” IEEE Trans. Inf. Theory 64, No. 6, 4024 (2018). DOI: 10.1109/TIT.2017.2717599.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Ding, M. Noshad, V. Tarokh, “Order selection of autoregressive processes using bridge criterion,” Proc. of IEEE Int. Conf. on Data Mining Workshop, ICDMW, 14–17 Nov. 2015, Atlantic City, NJ, USA (IEEE, 2015). DOI: 10.1109/ICDMW.2015.216.

    Google Scholar 

  13. Y. I. Abramovich, N. K. Spencer, M. D. E. Turley, “Order estimation and discrimination between stationary and time-varying (TVAR) autoregressive models,” IEEE Trans. Signal Process. 55, No. 6, 2861 (2007). DOI: 10.1109/TSP.2007.893966.

    Article  MathSciNet  MATH  Google Scholar 

  14. P. Stoica, Y. Selen, “Model-order selection: a review of information criterion rules,” IEEE Signal Processing Mag. 21, No. 4, 36 (2004). DOI: 10.1109/MSP.2004.1311138.

    Article  Google Scholar 

  15. V. V. Savchenko, “The principle of the information-divergence minimum in the problem of spectral analysis of the random time series under the condition of small observation samples,” Radiophys. Quantum Electronics 58, No. 5, 373 (2015). DOI: 10.1007/s11141-015-9611-4.

    Article  Google Scholar 

  16. S. S. Rachel, U. Snekhalatha, K. Vedhasorubini, D. Balakrishnan, “Spectral analysis of speech signal characteristics: a comparison between healthy controls and Laryngeal disorder,” in: Dash S., Das S., Panigrahi B. (eds). Int. Conf. on Intelligent Computing and Applications. Advances in Intelligent Systems and Computing (Springer, Singapore, 2018), Vol. 632. DOI: 10.1007/978-981-10-5520-1_31.

  17. A. V. Savchenko, “Sequential three-way decisions in efficient classification of piecewise stationary speech signals,” Lecture Notes in Artificial Intelligence 10314, 264 (2017). DOI: 10.1007/978-3-319-60840-2_19.

    Google Scholar 

  18. A. Esposito, M. Faundez-Zanuy, A. M. Esposito, G. Cordasco, Th. Drugman, J. Solé-Casals, F. C. Morabito, (eds.), Recent Advances in Nonlinear Speech Processing (Springer, 2016). DOI: 10.1007/978-3-319-28109-4.

    Google Scholar 

  19. M. H. Farouk, “Spectral analysis of speech signal and pitch estimation,” in: Application of Wavelets in Speech Processing (Springer, Cham, 2018). DOI: 10.1007/978- 3-319-69002-5_4.

    Chapter  Google Scholar 

  20. V. V. Savchenko, “Criterion for minimum of mean information deviation for distinguishing random signals with similar characteristics,” Radioelectron. Commun. Syst. 61, No. 9, 419 (2018). DOI: 10.3103/S0735272718090042.

    Article  Google Scholar 

  21. S. Kullback, Information Theory and Statistics (Dover Pub., N.Y., 1997).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nizhny Novgorod State Linguistic University, Nizhny Novgorod, Russia

    V. V. Savchenko

  2. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    A. V. Savchenko

Authors
  1. V. V. Savchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Savchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. V. Savchenko or A. V. Savchenko.

Additional information

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional Information

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/S0021347019050042 with DOI: https://doi.org/10.20535/S0021347019050042.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Savchenko, V.V., Savchenko, A.V. Criterion of Significance Level for Selection of Order of Spectral Estimation of Entropy Maximum. Radioelectron.Commun.Syst. 62, 223–231 (2019). https://doi.org/10.3103/S0735272719050042

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0735272719050042

Search

Navigation