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The envelope-based cyclic periodogram

机译：基于包络的循环周期图

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Cyclostationary analysis has proven effective in identifying signal components for diagnostic purposes. A key descriptor in this framework is the cyclic power spectrum, traditionally estimated by the averaged cyclic periodogram and the smoothed cyclic periodogram. A lengthy debate about the best estimator finally found a solution in a cornerstone work by Antoni, who proposed a unified form for the two families, thus allowing a detailed statistical study of their properties. Since then, the focus of cyclostationary research has shifted towards algorithms, in terms of computational efficiency and simplicity of implementation. Traditional algorithms have proven computationally inefficient and the sophisticated "cyclostationary" definition of these estimators slowed their spread in the industry. The only attempt to increase the computational efficiency of cyclostationary estimators is represented by the cyclic modulation spectrum. This indicator exploits the relationship between cyclostationarity and envelope analysis. The link with envelope analysis allows a leap in computational efficiency and provides a "way in" for the understanding by industrial engineers. However, the new estimator lies outside the unified form described above and an unbiased version of the indicator has not been proposed. This paper will therefore extend the analysis of envelope-based estimators of the cyclic spectrum, proposing a new approach to include them in the unified form of cyclostationary estimators. This will enable the definition of a new envelope-based algorithm and the detailed analysis of the properties of the cyclic modulation spectrum. The computational efficiency of envelope-based algorithms will be also discussed quantitatively for the first time in comparison with the averaged cyclic periodogram. Finally, the algorithms will be validated with numerical and experimental examples.
机译：事实证明，循环平稳分析可以有效地识别信号成分以进行诊断。该框架中的关键描述符是循环功率谱，传统上是通过平均循环周期图和平滑循环周期图来估算的。关于最佳估计量的冗长辩论最终在安东尼的基石工作中找到了解决方案，后者提出了两个家族的统一形式，从而可以对其属性进行详细的统计研究。从那时起，就计算效率和实现的简便性而言，循环平稳研究的重点已转向算法。传统算法已证明计算效率低下，这些估算器的复杂“循环平稳”定义减慢了它们在业界的普及。提高循环平稳估计量的计算效率的唯一尝试是由循环调制频谱表示的。该指标利用了循环平稳性与包络分析之间的关系。与包络分析的链接使计算效率有了飞跃，并为工业工程师的理解提供了一条“途径”。但是，新的估算器不在上述统一形式的范围内，尚未提出该指标的无偏版本。因此，本文将扩展对循环频谱基于包络的估计量的分析，并提出一种新方法，将其纳入循环平稳估计量的统一形式。这将有助于定义新的基于包络的算法，并详细分析循环调制频谱的特性。与平均循环周期图相比，基于包络的算法的计算效率也将首次进行定量讨论。最后，将通过数值和实验示例对算法进行验证。

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