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Acta Optica Sinica, Volume. 40, Issue 3, 0307001(2020)

Improved Triangular Window Apodization Function Based on Zero-Order Bessel Function

Jinglan Deng1,2, Jingjing Tong1、*, Minguang Gao1, Xiangxian Li1, Yan Li1, Xin Han1, and Wenqing Liu1
Author Affiliations
  • 1Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, Anhui 230031, China
  • 2University of Science and Technology of China, Hefei, Anhui 230026, China
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    AbstractGet PDF(in Chinese)
    Figures&Tables (8)
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    References (17)
    Cited By (5)
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    Figures & Tables(8)
    Time-frequency domain analysis of triangular window and improved triangular window apodization functions. (a) Time domain; (b) frequency domain

    Fig. 1. Time-frequency domain analysis of triangular window and improved triangular window apodization functions. (a) Time domain; (b) frequency domain

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    Working principle of portable Fourier transform infrared spectrometer

    Fig. 2. Working principle of portable Fourier transform infrared spectrometer

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    Spectra of different apodization functions. (a) Kaiser window with different parameters; (b) other common apodization functions

    Fig. 3. Spectra of different apodization functions. (a) Kaiser window with different parameters; (b) other common apodization functions

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    Results after data processing by Kaiser window apodization function with different parameters. (a) Original signal; (b) β=1; (c) β=4; (d) β=9; (e) β=16; (f) β=25

    Fig. 4. Results after data processing by Kaiser window apodization function with different parameters. (a) Original signal; (b) β=1; (c) β=4; (d) β=9; (e) β=16; (f) β=25

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    Results after data processing by different apodization functions. (a) Original signal; (b) triangular window; (c) Hanning window; (d) Hamming window; (e) Blackman window; (f) improved triangular window

    Fig. 5. Results after data processing by different apodization functions. (a) Original signal; (b) triangular window; (c) Hanning window; (d) Hamming window; (e) Blackman window; (f) improved triangular window

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    • Table 1. Mainlobe width and relative sidelobe attenuation of different apodization functions

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      Table 1. Mainlobe width and relative sidelobe attenuation of different apodization functions

      Apodization functionRelative sidelobe attenuation /dBMainlobe width
      Kaiser (β=1)-14.70.027π
      Kaiser (β=4)-30.60.035π
      Kaiser (β=9)-66.00.051π
      Kaiser (β=16)-122.00.066π
      Kaiser (β=25)-201.30.082π
      Rectangular-13.30.027π
      Triangular-26.60.039π
      Hanning-31.50.043π
      Hamming-42.50.039π
      Blackman-58.10.051π
      Improved triangular-28.50.043π

    • Table 2. Signal-to-noise ratio of Kaiser window apodization function with different parameters

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      Table 2. Signal-to-noise ratio of Kaiser window apodization function with different parameters

      Kaiser windowTest 1Test 2Test 3Average
      β=1RSN-PP6.080×1035.121×1036.600×1035.934×103
      RSN-RMS2.854×1042.401×1043.092×1042.782×104
      β=4RSN-PP7.859×1038.172×1037.902×1037.978×103
      RSN-RMS3.604×1043.664×1043.596×1043.621×104
      β=9RSN-PP9.320×1039.716×1039.051×1039.362×103
      RSN-RMS4.066×1044.334×1043.850×1044.083×104
      β=16RSN-PP1.030×1041.088×1049.968×1031.038×104
      RSN-RMS4.416×1044.744×1043.600×1044.253×104
      β=25RSN-PP1.095×1041.188×1041.066×1041.116×104
      RSN-RMS4.681×1045.065×1044.084×1044.610×104

    • Table 3. Signal-to-noise ratio of common apodization functions

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      Table 3. Signal-to-noise ratio of common apodization functions

      Apodization functionTest 1Test 2Test 3Average
      Original signalRSN-PP5.613×1034.613×1036.270×1035.499×103
      RSN-RMS2.680×1042.155×1042.955×1042.597×104
      TriangularRSN-PP8.751×1039.239×1038.605×1038.865×103
      RSN-RMS3.934×1044.121×1043.785×1043.947×104
      HanningRSN-PP8.443×1038.697×1038.427×1038.522×103
      RSN-RMS3.806×1043.987×1043.715×1043.836×104
      HammingRSN-PP8.285×1038.643×1038.237×1038.388×103
      RSN-RMS3.742×1043.877×1043.679×1043.766×104
      BlackmanRSN-PP9.240×1039.603×1038.985×1039.276×103
      RSN-RMS4.040×1044.300×1043.837×1044.059×104
      Improved triangularRSN-PP9.208×1039.721×1038.964×1039.298×103
      RSN-RMS4.071×1044.330×1043.853×1044.085×104
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    Jinglan Deng, Jingjing Tong, Minguang Gao, Xiangxian Li, Yan Li, Xin Han, Wenqing Liu. Improved Triangular Window Apodization Function Based on Zero-Order Bessel Function[J]. Acta Optica Sinica, 2020, 40(3): 0307001

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    Paper Information

    Category: Fourier Optics and Signal Processing

    Received: Jul. 30, 2019

    Accepted: Sep. 30, 2019

    Published Online: Feb. 10, 2020

    The Author Email: Tong Jingjing (jjtong@aiofm.ac.cn)

    DOI:10.3788/AOS202040.0307001

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology