关于谐波随机过程的四阶平稳性与四阶遍历性的一个结果

A Result for Fourth-Order Stationarity and Ergodicity of a Harmonic Random Process

本文分析了由随机谐波构成的复信号的四阶矩之有限数据估计，得到了四阶平稳和四阶遍历的条件，给出了估计误差及其方差，以及它们大样本的极限值的显式表达式，最后考虑了它的一个特例，说明这一情形下的方差由遍历部分和非遍历部分组成。

The finite data estimates of the complex fourth-order moments of a signal consisting of random harmonics are analysed.Conditions for the fourth-order stationarity and ergodicity are obtained.Explicit formulas for the estimation error and its variance as Well as their limiting large sample values are derived .Finally,these results are stated for a special case and the variance is shown to comprise an ergodic and a nonergodic part.