基于分数阶谱的频域广义白化滤波方法

Generalized whitening method based on fractional order spectrum in the frequency domain

在简要介绍稳定分布统计特性的基础上,描述了稳定分布的谱表示,提出了一种不同于二阶过程功率谱的共变谱密度概念及基于共变函数与共变谱密度的稳定分布白噪声的概念及其判断标准,对传统意义上的白噪声进行了广义化,并依据稳定分布的参数模型,论述了一种基于α谱的频域广义白化滤波方法。仿真实验表明,这种算法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白化滤波方法,是对传统的二阶统计量基础上的白化滤波方法的改造与推广。

This class of process had no close form of probability density function and finite second moment. The statistical characteristics of stable distribution was introduced, described its spectral representation, proposed a new different spectral density from power spectrum density of second order processes, thus a new concept of stable white noise and a method of whitening based on covariation spectrum under alpha-stable conditions were got. Simulation and analysis show that the method is robust and generalizes the conventional whitening filters based on second order statistics.