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

通信学报 ›› 2016, Vol. 37 ›› Issue (10): 1-8.doi: 10.11959/j.issn.1000-436x.2016189

• 学术论文 • 下一篇

确定性信号分解与平稳随机信号分解的统一研究

王宏禹,邱天爽

大连理工大学电子信息与电气工程学部，辽宁大连 116024

出版日期:2016-10-25 发布日期:2016-10-25
基金资助:
国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目

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

Hong-yu WANG,Tian-shuang QIU

Faculty of Electronic Information and Electrical Engineering,Dalian University of Technology,Dalian 116024,China

Online:2016-10-25 Published:2016-10-25
Supported by:
The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China

摘要/Abstract

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。

关键词: 信号分解, 线性系统, 正则稳定, 边界稳定, 线性空间, 正交投影, 自投影

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

王宏禹,邱天爽. 确定性信号分解与平稳随机信号分解的统一研究[J]. 通信学报, 2016, 37(10): 1-8.

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.

图/表 5

图1

图2

表1

g(k)与g(s)(k)的对比关系"

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), $g (k) = \sum_{i = 1}^{n} C_{i} λ_{i}^{k}$	$g^{(s)} (k) = \sum_{i = 1}^{n} [a_{i} \cos (k ω_{i} + φ_{i}) + b_{i} \sin (k ω_{i} + φ_{i})$

表1

图3

表2

参考文献 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}

确定性信号分解与平稳随机信号分解的统一研究

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

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