确定性信号分解与平稳随机信号分解的统一研究

摘要

对确定性信号分解与平稳随机信号分解进行了深入统一的研究。首先根据线性系统稳定性理论，分别给出正则稳定情况下与边界稳定情况下2种信号分解的统一研究结果。然后根据线性空间投影理论，分别给出正交投影情况下与自投影情况下2种信号分解的统一研究结果。前一种研究明确具体且物理意义清晰，后一种研究数学意义与几何意义清晰，将两者合在一起研究，相得益彰。%The unified decomposition theories and methods for deterministic signals and stationary random signals were deeply studied. According to the stability theory of linear systems, the unified results of signal decomposition under both regular stable and boundary stable conditions were given respectively. The unified results of signal decomposition under both orthogonal projection and self projection conditions were also provided based on the linear space projection theory. The former is clear and definite in its physical meaning, and the latter is clear in its mathematical and geometrical mean-ings. They are both complement with each other.