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中文摘要：
在简要介绍稳定分布统计特性的基础上,介绍了常用的信号非线性变换方法,建立不同于传统二阶过程的对数阶过程及其几何功率、几何相关、几何功率谱密度等新的信号分析概念,提出了一种新的稳定分布对数阶白噪声概念及其判断准则,建立了一种基于非线性变换的重拖尾稳定分布脉冲信号分析的新框架与模型。计算机模拟表明,这种模型是一种在高斯和分数低阶α稳定分布噪声条件下具有良好韧性的模型,是对传统的基于二阶统计量基础上的信号模型分析方法的改造与推广。
英文摘要：
Stable processes can better model the impulsive random signals and noises in physical observation. This paper briefly introduces the statistical characteristics of stable distribution and several nonlinear transform. We establish a kind of logarithmic- order processes and their geometric power, geometric correlation, geometric power spectral density. Thus we propose a new kind of signal processing framework and a new white noise. Simulation and analysis show that the model and framework is robust for stable distribution processes and generalizes the conventional second order power, correlation, power spectral density.
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