The Hilbert transform of mono- and multicomponent periodically non-stationary random signals (PNRSs), the carrier harmonics of which are narrow-band low-frequency modulated, are considered here. The relations for the auto- and cross-covariance and cross-spectral functions of a PNRS and its Hilbert transform are analyzed and the conditions for stationarity of the analytical signal are obtained. The covariance and spectral properties of the quadratures for monocomponent PNRS are analyzed, it is shown that correlation of the quadratures of a polycomponent PNRS causes the periodic non-stationarity of the analytic signal, and the specific features of this are mentioned. Extraction and analysis of the quadratures are carried out, and examples are given of the use of the Hilbert transform to analyze simulated and real-life polycomponent periodically non-stationary time series.

这里考虑单分量和多分量周期性非平稳随机信号 (PNRS) 的希尔伯特变换，其载波谐波是窄带低频调制的。分析了 PNRS 及其 Hilbert 变换的自协方差和互协方差以及互谱函数的关系，并获得了分析信号平稳性的条件。分析了单分量PNRS正交的协方差和频谱特性，表明多分量PNRS正交的相关性导致解析信号的周期性非平稳性，并提到了其具体特征。进行正交的提取和分析，