谱相关的数学关系与物理意义

doi:10.3969/j.issn.0372-2112.2015.04.027

电子学报 ›› 2015, Vol. 43 ›› Issue (4): 810-815.DOI: 10.3969/j.issn.0372-2112.2015.04.027

谱相关的数学关系与物理意义

王洪

电子科技大学电子工程学院, 四川成都 611731

收稿日期:2013-10-18 修回日期:2014-02-18 出版日期:2015-04-25
- 作者简介:
- 王洪男,1974年11月生,四川眉山人,副教授、硕士生导师.1996年、2003年、2007年分别在西北工业大学、重庆大学和电子科技大学获工学学士、工学硕士和工学博士学位.2007年至2009年在中国民航总局第二研究所从事博士后研究工作.2009年至2010年先后到纽约大学和新泽西理工大学访问学习.现为电子科技大学教师,主要从事统计信号处理、雷达信号处理、航空电子技术和高速实时信号处理等方面的研究工作.E-mail:hongw@uestc.edu.cn
- 基金资助:
- 国家自然科学基金 (No.61139003); 总装预研基金 (No.9140A17020812DZ02197); 中央高校科研基本业务费 (No.ZYGX2012J027); 科技部支撑计划 (No.2011BAH24B06,No.2011BAH24B05)

Mathematical Relationships and Physical Functions of Spectral Correlation

WANG Hong

School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

Received:2013-10-18 Revised:2014-02-18 Online:2015-04-25 Published:2015-04-25
- Supported by:
- National Natural Science Foundation of China (No.61139003); Pre-research Fund of the General Armaments Department (No.9140A17020812DZ02197); Fundamental Research Fund for Central University (No.ZYGX2012J027); Support Program of Ministry of Science and Technology (No.2011BAH24B06, No.2011BAH24B05)

摘要/Abstract

摘要：

周期性是自然现象和工程现象的基本特性之一,从复杂多变的、含有噪声的观测数据中发现周期性并测量其参数是信号处理的重要主题.谱相关是分析循环平稳信号二阶周期性的有力工具,本文研究谱相关的周期性解析功能的缘由、过程与特点.首先,梳理了谱相关理论体系中诸多重要概念之间的内在联系,建立了相互之间转换或映射的数学关系图;然后提出了按定义和转换关系逐步求解谱相关的方法.通过单周期信号的分析和每步操作效果与周期的对应关系,诠释了循环自相关、谱相关、无限循环谱和循环频率等重要概念的物理意义.

Abstract:

The periodicity is a feature of science and engineering phenomena,so detecting periodicity from complex and noise-included samples and measuring its parameters are important topics in signal processing.Spectral correlation is a useful tool to find second-order periodicity of cyclostationary signals.This paper investigates the reasons,procedures and features using spectral correlation to analyze cyclicity.First,internal relations between main definitions in spectral correlation theory are summarized and mathematic diagrams reflecting their transforming or mapping relations are built.Then a method to calculate spectral correlation based on the diagrams is proposed.By analysis of single periodic signals and connections between periods and results in each operation,physical functions of cyclic autocorrelation,spectral correlation,limit periodic spectrum and cyclic frequency,etc,are interpreted.

Key words: cyclostationary signals, spectral correlation, cyclic autocorrelation, second-order periodicity, Wigner-Ville distribution

中图分类号:

TN911.7

王洪. 谱相关的数学关系与物理意义[J]. 电子学报, 2015, 43(4): 810-815.

WANG Hong . Mathematical Relationships and Physical Functions of Spectral Correlation[J]. Acta Electronica Sinica, 2015, 43(4): 810-815.

参考文献

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谱相关的数学关系与物理意义

Mathematical Relationships and Physical Functions of Spectral Correlation

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