关于平稳序列的自相关矩阵的正定性

The Positiveness of Autocovariance Matrix of Stationary Sequence

平稳序列的自相关矩阵R(n)是非负定的。利用斯梯阶积分和纯跳跃函数的性质,本文通过积分谱F(ω)表达了R(n)为正定的充分必要条件,并得到了平稳过程的对偶结论。

The autocovariance matrix R(n) of a stationary sequence is nonnegative definite. Using properties of stieltjes integral and step function, we point out the necessary and sufficient condition for R(n) to be positive definite by means of its integrated spectrum F(w) in this paper. In addition, we obtain the parallel conclusion for stationary process.