确定性信号分解与平稳随机信号分解的统一研究

doi:10.11959/j.issn.1000-436x.2016189

Abstract

Abstract:

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 meanings.They are both complement with each other.

Key words: signal decomposition, linear system, regular stability, boundary stability, linear space, orthogonal projection, self projection

Hong-yu WANG,Tian-shuang QIU. Unified study on the decomposition for deterministic signals and stationary random signals[J]. Journal on Communications, 2016, 37(10): 1-8.

Figures/Tables 5

正则稳定线性系统g(k)	边界稳定线性系统g^(s)(k)
单位圆内一阶极点λ，	单位圆上一阶共轭极点
g(k)=λ^k	g ^(s)(k)=a cos kω+bsin kω
单位圆内 n 个不同极点	单位圆上单位圆内n个不同共轭极点
λi(i=1,2,…,n), $g (k) = \sum_{i = 1}^{n} C_{i} λ_{i}^{k}$	$g^{(s)} (k) = \sum_{i = 1}^{n} [a_{i} \cos (k ω_{i} + φ_{i}) + b_{i} \sin (k ω_{i} + φ_{i})$

References 15

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正交化过程	子空间扩大过程
{x ₁}?{ε₁}	x ₁=ε₁ ,H ₁ (X)=H ₁ (ε₁ ),span{x₁}=span{ε₁}
{x ₁ ,x ₂}?{ε₁ ,ε₂}	H ₂ (X)=H ₁ (X)⊕ε₂=span{x₁}⊕ε₂=span{ε₁ ,ε₂}
{x ₁ ,x ₂ ,x ₃}?{ε₁ ,ε₂ ,ε₃}	H ₃ (X)=H ₂ (X)⊕ε₃=span{ε₁ ,ε₂}⊕ε₃=span{ε₁ ,ε₂ ,ε₃}
…	…
{x ₁ ,x ₂ ,…,x _n}?{ε₁ ,ε₂ ,…,ε_n}	H _n (X)=H _n?1 (X)⊕ε_n=span{ε₁ ,ε₂ ,…,ε_n}

Unified study on the decomposition for deterministic signals and stationary random signals

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