随机信号双参数脉冲模型的分形特征

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

为了研究随机信号的统计特性,以幅度、宽度两个相对独立的特征参数为基本概念,建立随机信号的双参数脉冲模型.采用PCI-9812高速数据采集卡,对空气中悬浮颗粒随机性光散射脉冲信号、光电传感器本底噪声随机信号进行计数分布的统计分析.实验结果表明,随机性脉冲信号幅度、宽度子集的计数分布以很高的精度与以自然数为自变量的对数正态分布符合;进一步的计算结果表明,在脉冲信号幅度、宽度定义域内,随机脉冲信号集合的两个特征参数之间存在非线性变换关系,即随机信号的双参数统计分布具有非整数维分形特征.

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.