中文摘要：

提出了一种新的随机信号的非正交分解方法,通过对观测数据的二阶统计量所构成的矩阵进行正交变换,找到信号的特征空间,然后根据影响信号的实际因素,对信号进行非正交分解,得到更加符合实际,便于处理的分解结果.通过这样的分解,用一族非正交基函数表示一个随机信号,不仅可以知道该信号在各个基函数上所合成份的多少及其与已知信号的相似程度,还能够抓住决定信号表现的主要成份,去除噪声及次要成份.本文同时对这种非正交分解的收敛性作了分析.

英文摘要：

A new non-orthogonal decomposition method of random signal is proposed. This method finds the feature space of the signal by transforming the second-order statistics of the observation data at first. And then the non-orthogonal decomposition of the signal is performed according to the practical factors affecting the signal to obtain the decomposition results, which is more realistic and easy to deal with. Through this decomposition, a random signal can be re- presented by a family of non-orthogonal basis function. Therefore, the proportion of the ingre- dients contained by the signal can be known, the main component deciding the signal trend can be grasped, and the noise and minor component can be removed. Moreover, the convergence of the non-orthogonal decom position is analyzed.