谐波随机过程的四阶平稳性和四阶遍历性条件
CONDITIONS FOR FOURTH-ORDER STATIONARITY AND ERGODICITY OF A HARMONIC RANDOM PROCESS
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摘要: 本文分析了由随机谐波构成的复信号四阶矩的有限数据估计,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,以及它们大样本极限的显式表达式。最后考虑了相应于三次相位耦合的特例,说明这一情形下的方差由遍历和非遍历两部分组成。
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关键词:
- 谐波随机过程; 四阶平稳性; 四阶遍历性
Abstract: 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, a special case relevant to cubic phase coupling is considered, and these results are stated for this case, the variance is shown to comprise an ergodic and a nonergodic part. -
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