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The fractal character of two-parameter pulse model for random signal

Yang Juan Bian Bao-Min Peng Gang Li Zhen-Hua

The fractal character of two-parameter pulse model for random signal

Yang Juan, Bian Bao-Min, Peng Gang, Li Zhen-Hua
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  • For studying the statistical character of the random signal, the width and amplitude of two relatively independent characteristic parameters are used to establish the two-parameter pulse model of the random signal. On the basis of this, the counting distributions of random signal for aerosol’s scattering pulse and background noise of photoelectric sensor are statistically analyzed by using the high-speed data acquisition card PCI-9812. The experimental results show that the counting distributions of amplitude and width subsets for the random pulse signals match well with the form of the lognormal distribution while using the natural number as the independent variable. Further more, the calculating results indicate that the amplitude and width of the distribution have nonlinear transform relation in the field of definition of them for pulsed signal. Namely, the two parameters' statistical distributions have the fractal character with non-integral dimension.
    • Funds:
    [1]

    Jost H, Kikuo O, Thomas T 2004 Appl. Opt 43 5893

    [2]

    Wang Q H, Zhang Y Y, Lai J C, Li Z H, He A Z 2008 Acta Phys. Sin. 57 1203 (in Chinese)[王清华、张颖颖、来建成、李振华、贺安之 2008 物理学报 57 1203]

    [3]

    Alexei K, Heike W, Frank S 2005 Appl. Opt. 44 4693

    [4]

    Lekhtmakher S, Shapiro M 2004 Aerosol Science and Technology 38 155

    [5]

    Yang J, Lai X M, Peng G, Bian B B, Lu J 2009 Acta Physica Sin. 58 3008(in Chinese)[杨 娟、赖晓明、彭 刚、卞保民、陆 建 2009 物理学报 58 3008]

    [6]

    Qiao L F, Zhang Y M, Xie Q Y, Fang J, Wang J J 2007 Acta Phys. Sin. 56 6736 (in Chinese)[乔利锋、张永明、谢启源、方 俊、王进军 2007 物理学报 56 6736]

    [7]

    Ren X C, Guo L X 2008 Chin. Phys. B 17 2956

    [8]

    Xie T, He C, William P 2010 Chin. Phys. B 19 024101

    [9]

    Kiss L B, Soderlund J, Granqvist C G 1999 Fourth International Conference on Nanostructured Materials 12 327

    [10]

    Granqvist C G, Buhrman R A 1976 J. Appl. Phys. 47 2200

    [11]

    Baker L, Giancola A J, Allahdadi F 1992 J. Appl. Phys. 72 2724

    [12]

    Park D, An M, Hwang J 2007 Aerosol Science 38 1240

    [13]

    Park K T, Park D, Lee S G, Hwang J 2009 Aerosol Science 40 858

    [14]

    Mitzenmacher M 2004 Internet Mathematics 1 226

    [15]

    Peng G, Lai X M,Yan Z G, Bian B B, Lu J 2010 Acta Opt. Sin. 30 1693 (in Chinese)[彭 刚、赖小明、闫振纲、卞保民、陆 建 2010 光学学报 30 1693]

  • [1]

    Jost H, Kikuo O, Thomas T 2004 Appl. Opt 43 5893

    [2]

    Wang Q H, Zhang Y Y, Lai J C, Li Z H, He A Z 2008 Acta Phys. Sin. 57 1203 (in Chinese)[王清华、张颖颖、来建成、李振华、贺安之 2008 物理学报 57 1203]

    [3]

    Alexei K, Heike W, Frank S 2005 Appl. Opt. 44 4693

    [4]

    Lekhtmakher S, Shapiro M 2004 Aerosol Science and Technology 38 155

    [5]

    Yang J, Lai X M, Peng G, Bian B B, Lu J 2009 Acta Physica Sin. 58 3008(in Chinese)[杨 娟、赖晓明、彭 刚、卞保民、陆 建 2009 物理学报 58 3008]

    [6]

    Qiao L F, Zhang Y M, Xie Q Y, Fang J, Wang J J 2007 Acta Phys. Sin. 56 6736 (in Chinese)[乔利锋、张永明、谢启源、方 俊、王进军 2007 物理学报 56 6736]

    [7]

    Ren X C, Guo L X 2008 Chin. Phys. B 17 2956

    [8]

    Xie T, He C, William P 2010 Chin. Phys. B 19 024101

    [9]

    Kiss L B, Soderlund J, Granqvist C G 1999 Fourth International Conference on Nanostructured Materials 12 327

    [10]

    Granqvist C G, Buhrman R A 1976 J. Appl. Phys. 47 2200

    [11]

    Baker L, Giancola A J, Allahdadi F 1992 J. Appl. Phys. 72 2724

    [12]

    Park D, An M, Hwang J 2007 Aerosol Science 38 1240

    [13]

    Park K T, Park D, Lee S G, Hwang J 2009 Aerosol Science 40 858

    [14]

    Mitzenmacher M 2004 Internet Mathematics 1 226

    [15]

    Peng G, Lai X M,Yan Z G, Bian B B, Lu J 2010 Acta Opt. Sin. 30 1693 (in Chinese)[彭 刚、赖小明、闫振纲、卞保民、陆 建 2010 光学学报 30 1693]

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  • Received Date:  27 April 2010
  • Accepted Date:  05 May 2010
  • Published Online:  15 January 2011

The fractal character of two-parameter pulse model for random signal

  • 1. Department of Information Physics and Engineer, Nanjing University of Science and Technology, Nanjing 210094, China

Abstract: For studying the statistical character of the random signal, the width and amplitude of two relatively independent characteristic parameters are used to establish the two-parameter pulse model of the random signal. On the basis of this, the counting distributions of random signal for aerosol’s scattering pulse and background noise of photoelectric sensor are statistically analyzed by using the high-speed data acquisition card PCI-9812. The experimental results show that the counting distributions of amplitude and width subsets for the random pulse signals match well with the form of the lognormal distribution while using the natural number as the independent variable. Further more, the calculating results indicate that the amplitude and width of the distribution have nonlinear transform relation in the field of definition of them for pulsed signal. Namely, the two parameters' statistical distributions have the fractal character with non-integral dimension.

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