Wide-sense cyclostationary processes are an important class of non-stationary processes that have a periodic structure in their first- and second-order moments. This article extends the notion of cyclostationarity (in the wide sense) to processes where the mean and covariance functions might depart from strict periodicities and constant amplitudes. Specifically, we propose a novel and flexible class of processes that allows periods and amplitudes of the mean and covariance functions to evolve and, therefore, accommodates a much larger class of processes than the classical cyclostationary processes. Thereafter, we investigate its properties, provide methodologies for statistical inference, and illustrate the presented methods using synthetic signals and a physical signal, from the heavens, of the magnitudes of the light emitted from the variable star R Hydrae.

中文翻译：

---

周期和振幅不断变化的循环平稳过程

广义的循环平稳过程是一类重要的非平稳过程，其一阶和二阶矩具有周期性结构。本文将循环平稳性的概念（广义上）扩展到均值和协方差函数可能偏离严格的周期性和恒定振幅的过程。具体来说，我们提出了一种新颖而灵活的过程类别，该过程类别允许均值和协方差函数的周期和幅度演化，因此，与经典的循环平稳过程相比，它容纳的过程类别要大得多。之后，我们研究其性质，提供统计推断的方法，并说明使用合成信号和物理信号从天上来的方法，