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

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

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确定性信号分解与平稳随机信号分解的统一研究

学术论文 | 更新时间：2024-06-05

- 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
- 通信学报 2016年37卷第10期页码：1-8
- 作者机构：
  
  大连理工大学电子信息与电气工程学部，辽宁大连 116024
- 作者简介：
  
  [ "王宏禹（1929-），男，北京人，大连理工大学教授、博士生导师，主要研究方向为信号信息处理。" ]
  [ "邱天爽（1954-），男，江苏海门人，博士，大连理工大学教授、博士生导师，主要研究方向为信号信息处理。" ]
- 基金信息：
  
  国家自然科学基金资助项目(61172108);国家自然科学基金资助项目(61139001);国家自然科学基金资助项目(81241059);国家自然科学基金资助项目(61671105)
- DOI：10.11959/j.issn.1000-436x.2016189
  中图分类号： TN911.7
- 网络出版日期：2016-10，
  
  纸质出版日期：2016-10-25
- 稿件说明：
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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.
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. DOI： 10.11959/j.issn.1000-436x.2016189.

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

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。

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.

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references

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