多维并元平稳序列的并元滑动和表示

研究了多维并元平稳序列具有并元滑劝和表示的条件，利用多维并元平稳序列的谱定理和平方可积函数的Ｗｓｌｓｈ展开定理和以了以下定理：ｑ维并元平稳序列具有并元滑动和表示的充要条件是它的谱密度矩阵在且几乎处处有常微数ｒ。

The One -sided Dyadic Moving Average Representation of the Multidimensional Dyadic Stationary Sequence

The ultidimensional dyadic stationary sequence with a representation as a one-sided dyadic moving average is a kind of very important sequence in both theory and application. The purpose of this paper is to discuss what kind of multidimentsional dyadic stationary sequence bas such a representation. By the theorems of the multidimensional dyadic stationary sequence and the Walsh expansion theorem of the square integrable fuaction, the following result can be obtained in this paper: A q-dimension dyadic stationary sequence bas a representation as a one- sided dyadic moving average if and only if the sequence has a spectral density matrix with the con- Stant rank m, a.e., [Lebesgue measure].