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Based on the random process of the photodetector noise signals {Vi}, the different characteristics of the two parts of the random measurementstability constant part and random fluctuation part are analyzed. A new mathematical model of the random noise signal is established. The theoretical analysis shows that the statistical distributions must obey the relationship of nonlinear transform. The distribution laws of the different characteristic quantities in the same random process are studied experimentally, such as, the amplitude of extreme, the amplitudes of the rising edge and falling edge, the interval between extreme points, the difference between adjacent amplitudes, the product value of the quantities and the quotient value of the quantities. And the statistical distribution of these characteristic quantities matches well with the form of the lognormal distribution. From the theoretical and experimental results we can conclude that the lognormal distribution plays an important role in describing the random fluctuation part characteristic of random process.
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Keywords:
- noise signal /
- random fluctuations /
- lognormal distribution
[1] Kristensen D, Mele A 2011 J. Financ. Econ. 102 390
[2] Wang Q, Li L, Hu J M, Zou B 2011 J. Tsinghua Univ. (Sci. Tech.) 51 309 (in Chinese) [王祺, 李力, 胡坚明, 邹斌 2011 清华大学学报(自然科学版) 51 309]
[3] Torío P, Sánche M G 2009 IEEE Trans. Consumer Electron. 55 1798
[4] Torío P, Sánchez M G 2007 IEEE Trans. Vehicul. Technol. 56 2844
[5] Peng G, Lai X M, Yan Z G, Bian B M, Lu J 2010 Acta Opt. Sin. 30 6 (in Chinese) [彭刚, 赖小明, 闫振纲, 卞保民, 陆建 2010 光学学报 30 6]
[6] Yang J, Bian B M, 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]
[7] Yang J, Bian B M, Yan Z G, Wang C Y, Li Z H 2011 Acta Phys. Sin. 60 100506 (in Chinese) [杨娟, 卞保民, 闫振纲, 王春勇, 李振华 2011 物理学报 60 100506]
[8] Lin Y L, Yan Z G, Wang C Y, Bian B M 2012 Acta Phys. Sin. 61 100505 (in Chinese) [林颖璐, 闫振纲, 王春勇, 卞保民 2012 物理学报 61 100505]
[9] Huang X N 2000 J. Qinghai Normal Univ. (Natural Science) 4 48 (in Chinese) [黄湘宁 2000 青海师范大学学报 4 48]
[10] Guo C L, Sun J J, Fang R C 2003 Opt. Tech. 29 636 (in Chinese) [郭从良, 孙金军, 方容川 2003 光学技术 29 636]
[11] Shu X M, Fang J, Shen S F, Liu Y J, Yuan H Y, Fan W C 2006 Acta Phys. Sin. 55 4466 (in Chinese) [疏学明, 方俊, 申世飞, 刘勇进, 袁宏永, 范维澄 2006 物理学报 55 4466]
[12] Xu M, Alfano R R 2005 Opt. Lett. 30 3051
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[1] Kristensen D, Mele A 2011 J. Financ. Econ. 102 390
[2] Wang Q, Li L, Hu J M, Zou B 2011 J. Tsinghua Univ. (Sci. Tech.) 51 309 (in Chinese) [王祺, 李力, 胡坚明, 邹斌 2011 清华大学学报(自然科学版) 51 309]
[3] Torío P, Sánche M G 2009 IEEE Trans. Consumer Electron. 55 1798
[4] Torío P, Sánchez M G 2007 IEEE Trans. Vehicul. Technol. 56 2844
[5] Peng G, Lai X M, Yan Z G, Bian B M, Lu J 2010 Acta Opt. Sin. 30 6 (in Chinese) [彭刚, 赖小明, 闫振纲, 卞保民, 陆建 2010 光学学报 30 6]
[6] Yang J, Bian B M, 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]
[7] Yang J, Bian B M, Yan Z G, Wang C Y, Li Z H 2011 Acta Phys. Sin. 60 100506 (in Chinese) [杨娟, 卞保民, 闫振纲, 王春勇, 李振华 2011 物理学报 60 100506]
[8] Lin Y L, Yan Z G, Wang C Y, Bian B M 2012 Acta Phys. Sin. 61 100505 (in Chinese) [林颖璐, 闫振纲, 王春勇, 卞保民 2012 物理学报 61 100505]
[9] Huang X N 2000 J. Qinghai Normal Univ. (Natural Science) 4 48 (in Chinese) [黄湘宁 2000 青海师范大学学报 4 48]
[10] Guo C L, Sun J J, Fang R C 2003 Opt. Tech. 29 636 (in Chinese) [郭从良, 孙金军, 方容川 2003 光学技术 29 636]
[11] Shu X M, Fang J, Shen S F, Liu Y J, Yuan H Y, Fan W C 2006 Acta Phys. Sin. 55 4466 (in Chinese) [疏学明, 方俊, 申世飞, 刘勇进, 袁宏永, 范维澄 2006 物理学报 55 4466]
[12] Xu M, Alfano R R 2005 Opt. Lett. 30 3051
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