谐波随机过程的高阶平稳性和高阶遍历性条件

Conditions for Higher-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高阶矩的有限数据估计，得到了高阶平稳和高阶遍历条件，给出了估计误差及其方差，以及它们大样本极限值的显式表达式。最后考虑了文献［２］中的情形，说明文献［２］中所得结果为本文的特例。

The finite data estimates of the higher-order moments of a complex signal consisting of random harmonics are analysed. Conditions for the higher-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,the results in reference[2] are shown to be a special case of this paper.