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A two-parameter statistical model of the pulsed signals which can be used to describe the basic structural characteristics of the random signals is established in this paper. As a result, the random signal counting distributions of amplitude q(lV) and width p(l), as well as the different signal subset counting distributions under given width l(lV) and amplitude lV(l), all match well with the form of the lognormal distribution with a natural numberused as an independent variable. Besides, it is also found that there are internal relations between the counting distribution statistical characteristic parameters lnV, ln, lnV, ln and the corresponding signal characteristic parameters lV and l. In essence, these relations are the representations of random signal fractal characteristics. In a word, two characteristic parameter statistical distributions of the random signals each have a non-integral dimensional fractal feature.
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Keywords:
- fractal /
- random signal /
- two-parameter /
- statistical
[1] Mandelbrot B B 1982 The Fractal Geometry of Nature(San Francisco: W.H.Freeman)
[2] Tasdemir A 2009 Minerals Engineering 22 156
[3] [4] [5] Ren X C, Guo L X 2008 Chin. Phys. B 17 2956
[6] [7] Zhao J, Lei L, Pu X Q 2008 Fractal Theory and Its Application in Signal Processing (Beijing: Tsinghua University Press) p3(in Chinese)[赵 健、雷 蕾、蒲小勤 2008 分形理论及其在信号处理中的应用(北京:清华大学出版社) 第3页]
[8] [9] Ma Q L, Bian C H, Wang J 2010 Acta Phys. Sin. 59 4480 (in Chinese)[马千里、卞春华、王 俊 2010 物理学报 59 4480]
[10] Han J J, Fu W J 2010 Chin. Phys. B 19 010205
[11] [12] [13] Kiss L B, Soderlund J, Granqvist C G 1999 NanoStructured Materials 12 327
[14] [15] Park D, An M, Hwang J 2007 Aerosol Science 38 420
[16] Millan H, Gonzalez-Posada M, Aguilar M, Dominguez J, Cespedes L 2003 Geoderma 117 117
[17] [18] [19] Kim Y, Sievering H, Boatman J, Wellman D, Pszenny A 1995 J.Geophys. Res. 100 23027
[20] [21] Michael D H 2006 Journal of Volcanology and Geothermal Research 154 8
[22] [23] Tijana B, Aleksandra V, Aleksandar K 2010 Journal of Theoretical Biology 262 214
[24] Yang J, Bian B B, Peng G, Yan Z G, Li Z H 2010 Acta Phys. Sin. 59 7713 (in Chinese)[杨 娟、卞保民、彭 刚、闫振纲、李振华 2010 物理学报 59 7713]
[25] [26] [27] Peng G, Lai X M,Yan Z G, Bian B B, Lu J 2009 Acta Optica Sinica 30 1693 (in Chinese)[彭 刚、赖小明、闫振纲、卞保民、陆 建 2009 光学学报 30 1693]
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[1] Mandelbrot B B 1982 The Fractal Geometry of Nature(San Francisco: W.H.Freeman)
[2] Tasdemir A 2009 Minerals Engineering 22 156
[3] [4] [5] Ren X C, Guo L X 2008 Chin. Phys. B 17 2956
[6] [7] Zhao J, Lei L, Pu X Q 2008 Fractal Theory and Its Application in Signal Processing (Beijing: Tsinghua University Press) p3(in Chinese)[赵 健、雷 蕾、蒲小勤 2008 分形理论及其在信号处理中的应用(北京:清华大学出版社) 第3页]
[8] [9] Ma Q L, Bian C H, Wang J 2010 Acta Phys. Sin. 59 4480 (in Chinese)[马千里、卞春华、王 俊 2010 物理学报 59 4480]
[10] Han J J, Fu W J 2010 Chin. Phys. B 19 010205
[11] [12] [13] Kiss L B, Soderlund J, Granqvist C G 1999 NanoStructured Materials 12 327
[14] [15] Park D, An M, Hwang J 2007 Aerosol Science 38 420
[16] Millan H, Gonzalez-Posada M, Aguilar M, Dominguez J, Cespedes L 2003 Geoderma 117 117
[17] [18] [19] Kim Y, Sievering H, Boatman J, Wellman D, Pszenny A 1995 J.Geophys. Res. 100 23027
[20] [21] Michael D H 2006 Journal of Volcanology and Geothermal Research 154 8
[22] [23] Tijana B, Aleksandra V, Aleksandar K 2010 Journal of Theoretical Biology 262 214
[24] Yang J, Bian B B, Peng G, Yan Z G, Li Z H 2010 Acta Phys. Sin. 59 7713 (in Chinese)[杨 娟、卞保民、彭 刚、闫振纲、李振华 2010 物理学报 59 7713]
[25] [26] [27] Peng G, Lai X M,Yan Z G, Bian B B, Lu J 2009 Acta Optica Sinica 30 1693 (in Chinese)[彭 刚、赖小明、闫振纲、卞保民、陆 建 2009 光学学报 30 1693]
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