非平稳随机过程功率谱与自相关的关系推导  

Analysis of the Relationship Between the Power Spectral Density of Non-stochastic Processes and Its Autocorrelation Function

作　　者：胡敬安[1] 魏冬梅[1] HU Jing′an;WEI Dongmei(School of Physics and Electronics,Shandong Normal University,Jinan Shandong 250014)

机构地区：[1]山东师范大学物理与电子科学学院,山东济南250014

出　　处：《首都师范大学学报（自然科学版）》2020年第2期20-22,共3页Journal of Capital Normal University：Natural Science Edition

摘　　要：涉及随机过程的文献或书籍通常只介绍广义平稳随机过程的功率谱密度与自相关函数的关系,即佩利-维纳准则.本文就非平稳随机过程的功率谱与自相关之间的关系进行了推导,结论是功率谱密度与自相关函数的时间平均是1对傅立叶变换.Literature and books related to stochastic processes usually only introduce the relationship between power spectral density(PSD)of wide-sense stationary random processes and its autocorrelation function,i.e.Pellet-Wiener criterion.The relationship between PSD of non-stochastic processes and its autocorrelation function is analyzed.The conclusion is that PSD and the time average of the autocorrelation function is a Fourier transform pair.

关 键 词：随机过程 平均自相关 功率谱密度 

分 类 号：TN911.1[电子电信—通信与信息系统]