A family of flat-top windows with low spectrum sidelobes for harmonic analysis of signals

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Abstract

Flat-top windows intended to reduce spectrum amplitude measurement error in discrete harmonic analysis are considered. A new family of flat-top windows, which provide the minimum level of the highest spectrum sidelobe and low calculation complexity is proposed. Mathematical representation of the new windows and a method of optimization of their parameters, which rely on authors’ earlier works are described. A number of flat-top windows of orders 1…6 and sidelobe falloff rates of 6, 12, 18, 24, 30, 36, and 48 decibels per octave are synthesized, tables of their parameters are provided, and their characteristics are analyzed. An alternative technique to reduce the spectrum amplitude measurement error is proposed.

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About the authors

G. V. Zaytsev

«Almaz» Research and Production Corporation

Author for correspondence.
Email: gennady-zaytsev@yandex.ru
Russian Federation, Leningradskii prosp., 80, Build. 16, Moscow, 125190

A. D. Khzmalyan

«Almaz» Research and Production Corporation

Email: gennady-zaytsev@yandex.ru
Russian Federation, Leningradskii prosp., 80, Build. 16, Moscow, 125190

References

  1. Хэррис Ф.Дж. // ТИИЭР. 1978. Т. 66. № 1. С. 60.
  2. Prabhu K.M.M. Window Functions and Their Applications in Signal Processing. Boca Raton: CRC Press, 2014.
  3. Оппенгейм А.В., Шафер Р.В. Цифровая обработка сигналов. М.: Техносфера, 2006.
  4. D’Antona G., Ferrero A. Digital Signal Processing for Measurement Systems. N.Y.: Springer Media, 2006.
  5. Salvatore, L., Trotta A. // IEE Proc. 1988. V. 135. № 6. P. 346.
  6. Heinzel G., Rudiger A., Schilling R. Spectrum and Spectral Density Estimation by the Discrete Fourier transform (DFT), Including a Comprehensive List of Window Functions and Some New at-top Windows. Hannover: Max-Planck-Institut fur Gravitationsphysik, Teilinstitut. 2002, 84 p.
  7. Cortés C.A., Mombello E., Dib R., Ratta G. // Signal Processing. 2007. V. 87. P. 2151.
  8. Зайцев Г.В. // Радиотехника. 2011. № 3. С. 21.
  9. Коллатц Л., Крабс В. Теория приближений. Чебышевские приближения и их приложения. М.: Наука, 1978.
  10. Зайцев Г.В. // Радиотехника. 2012. № 1. С. 55.
  11. Хзмалян А.Д. // Вестник воздушно-космической обороны. 2018. № 4. С. 90.
  12. Zaytsev G.V., Khzmalyan A.D. // Proc. Int. Conf. on Eng. and Telecom. (EnT). Dolgoprudny. 20–21 Nov. 2019. N.Y.: IEEE, 2019. https://doi.org/10.1109/EnT47717.2019.9030552
  13. Зайцев Г.В., Хзмалян А.Д. // РЭ. 2021. Т. 66. № 5. С. 443. https://doi.org/10.31857/S0033849421050120
  14. Зайцев Г.В., Хзмалян А.Д. Оптимальные весовые функции для гармонического анализа сигналов в реальном времени. М.: НПО «Алмаз», 2023. https://elibrary.ru/item.asp?id=54363389

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2. Fig. 1. View of the weight function with a flat top: a - in the time domain; b - in the frequency domain; c - spectrum at the flattening interval.

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3. Fig. 2. Dependence of the error δ at the flattening interval on the synthesis parameter β for optimal cosine-polynomial functions with side lobe decay rates of 6 (1), 24 (2), and 36 dB/oct (3).

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4. Fig. 3. Dependences of maximum side lobe levels on the segment [β, N / 2] bin on the parameter β for optimal weight functions with a flat top (1, 2) and without this property (3, 4) for side lobe decay rates of 6 (1, 3) and 24 dB/oct (2, 4).

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