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Class of Optimal Polynomial Window Functions for Spectral Analysis of Signals

  • THEORY AND METHODS OF SIGNAL PROCESSING
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Abstract

The problem of synthesis of low-order polynomial window functions with an arbitrarily specified decay rate of spectral lobes (optimal with respect to minimization of the maximum side lobe on a specified segment of the frequency axis) is solved. A method for the synthesis of optimal functions with verification of the solution is developed. The window functions of orders 1–12 with side-lobe decay rates of 6, 12, 18, 24, and 30 dB/oct are synthesized and tables of the parameters are presented. The characteristics of the functions are analyzed and compared with the known ones. A simple algorithm for calculation of the synthesized functions is proposed.

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REFERENCES

  1. F. J. Harris, Proc. IEEE 66, 51–83 (1978).

    Article  Google Scholar 

  2. A. H. Nuttall, IEEE Trans. Acoust., Speech, Signal Process. 29, 84 (1981).

    Article  Google Scholar 

  3. H.-H. Albrecht, The Open Signal Processing J. 3, 20 (2010).

    Article  Google Scholar 

  4. G. V. Zaitsev, Radiotekhnika, No. 3, 21 (2011).

  5. G. V. Zaitsev, Radiotekhnika, No. 1, 55 (2012).

  6. A. D. Khzmalyan, Vestn. VKO, No. 4 (20), 90 (2018).

    Google Scholar 

  7. G. V. Zaytsev and A. D. Khzmalyan, in Proc. 5th Int. Conf. on Eng. and Telecom., Moscow, Nov. 15–16, 2018 (IEEE, New York, 2019). https://doi.org/10.1109/EnT-MIPT.2018.00030

  8. G. V. Zaytsev and A. D. Khzmalyan, J. Commun. Technol. Electron. 65, 502 (2020). https://doi.org/10.1134/S1064226920050137

    Article  Google Scholar 

  9. G. V. Zaytsev and A. D. Khzmalyan, in Proc. 2019 Int. Conf. on Eng. and Telecom., Dolgoprudny, Russia, Nov. 20–21, 2019 (IEEE, New York, 2019), p. 9030552. https://doi.org/10.1109/EnT47717.2019.9030552

  10. G. V. Zaytsev and A. D. Khzmalyan, Tsifr. Obrabotka Sign., No. 2, 35 (2019).

  11. R. G. Kulkarni, Signal Processing 83, 1145 (2003).

    Article  Google Scholar 

  12. K. Okarma, Signal Processing 87, 782 (2007).

    Article  Google Scholar 

  13. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing, (Englewood Cliffs, New York, 1979; Tekhnosfera, Moscow, 2006).

  14. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Nauka, Moscow, 1963; Academic, New York, 1980).

  15. L. Collatz and W. Krabs, Approximations Theorie. Tschebyscheffsche Approximation mit Anwendungen (Teubner Studien Bucher, Stuttgart, 1972; Nauka, Moscow, 1978).

  16. D. P. Bertsekas, Convex Optimization Algorithms (Athena Scientific, Belmont. Mass., USA, 2015).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Scientific Industrial Enterprise Almaz, 125190, Moscow, Russia

    G. V. Zaitsev & A. D. Khzmalyan

Authors
  1. G. V. Zaitsev
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  2. A. D. Khzmalyan
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Correspondence to G. V. Zaitsev or A. D. Khzmalyan.

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Translated by A. Chikishev

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Zaitsev, G.V., Khzmalyan, A.D. Class of Optimal Polynomial Window Functions for Spectral Analysis of Signals. J. Commun. Technol. Electron. 66, 567–580 (2021). https://doi.org/10.1134/S1064226921050107

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  • DOI: https://doi.org/10.1134/S1064226921050107

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