Two classes of window functions

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Two new classes of window functions, a special case of each of which is the Kaiser window taken as a sample, are proposed and investigated. In each class, we experimentally find suboptimal windows with the level of the maximum side lobe of the spectrum smaller than that of a sample with the same main lobe width and window duration.

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作者简介

Z. Lerner

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Email: lerner269@gmail.com
俄罗斯联邦

参考

  1. Дворкович В.П., Дворкович А.В. Оконные функции для гармонического анализа сигналов. М.: Техносфера, 2016.
  2. Корн Г., Корн Т. Справочник по математике. М.: Физматлит, 1970.
  3. Диткин В.А., Прудников А.П. Интегральные преобразования и операционное исчисление. М.: Физматлит, 1961

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2. Fig. 1. Window functions of the suboptimal φ-class window for α = 3.07 (1), 4.05 (3) and 5.02 (5), Kaiser window functions for αk = 3 (2), 4 (4) and 5 (6), for all curves ≤ = 1.

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3. Fig. 2. Spectra of the window function of the suboptimal φ-class window for α = 3.07 (1) and the Kaiser window function for αk = 3 (2), for both curves β = 1.

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4. Fig. 3. Spectra of the window function of the suboptimal φ-class window for α = 4.05 (1) and the Kaiser window function for αk = 4 (2), for both curves β = 1.

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5. Fig. 4. Spectra of the window function of the suboptimal φ-class window for α = 5.02 (1) and the Kaiser window function for αk = 5 (2), for both curves β = 1.

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6. Fig. 5. Spectra of the window function of the suboptimal Ψ-class window for α = α = 3.1225 (1) and the Kaiser window function for αk = 3 (2), for both curves β = 1.

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7. Fig. 6. Spectra of the window function of the suboptimal Ψ-class window for α = 4.0927 (1) and the Kaiser window function for αk = 4 (2), for both curves β = 1.

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8. Fig. 7. Spectra of the window function of the suboptimal Ψ-class window for α = 5.0744 (1) and the Kaiser window function for αk = 5 (2), for both curves β = 1.

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9. Fig. 8. Window functions of the suboptimal window of the Ψ-class for α = 3.1225 (1) and 4.0927 (3), Kaiser window functions for αk = 3 (2) and 4 (4), for all curves β = 1, the scale on the ordinate axis is linear (a) and logarithmic (b).

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10. Fig. 9. Window functions of the suboptimal window of the Ψ-class: α = 5.0744 for β = 1 (1) and 1.5 (3); Kaiser window functions: αk = 5 for β = 1 (2) and 1.5 (4); for all curves, the scale along the ordinate axis is linear (a) and logarithmic (b).

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11. Fig. 10. Spectra of window functions of the suboptimal window of the Ψ-class: α = 5.0744 for β = 1 (1) and 1.5 (3); spectra of window functions of the Kaiser window: αk = 5 for β = 1 (2) and 1.5 (4).

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12. Appendix
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