通信学报2018，Vol.39Issue(12)：1-9,9.DOI:10.11959/j.issn.1000-436x.2018219
信号特征谱表示与平稳随机信号谱分解统一的研究
Unified study on characteristic spectrum representation of signals and spectral decomposition for stationary random signals
摘要
Abstract
The unified relationship between the signal characteristic spectrum representation and the spectral decomposition for the stationary random signal was deeply studied. By using the relations among the differential operators, the integral operator and the Green's function of the characteristic differential equation, the inverse relationship between the Hermitian differential operator and the Hermitian integral operator were given, the characteristic differential equation and corresponding characteristic integral equation were demonstrated, and the spectral representations of both Hermitian differential and integral operators and the general spectral representations for both operators were provided. Based on the superposition method of the stochastic simple harmonic vibration and the Hilbert space unitary operator method for the stationary random signal spectral decomposition, the connection and unification on mathematics of the signal characteristic spectral representation and the stationary random signal spectral decomposition are revealed.关键词
格林函数/厄尔密特算子/微分算子/积分算子/正交投影算子/谱表示/酉算子/谱分解Key words
Green function/ Hermitian operator/ differential operator/ integral operator/ orthogonal projection operator/ spectral representation/ unitary operator/ spectral decomposition分类
信息技术与安全科学引用本文复制引用
王宏禹,邱天爽..信号特征谱表示与平稳随机信号谱分解统一的研究[J].通信学报,2018,39(12):1-9,9.基金项目
国家自然科学基金资助项目(No.61671105,No.61172108,No.61139001) （No.61671105,No.61172108,No.61139001）
