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Cyclic spectral analysis in practice

机译：实践中的循环光谱分析

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This paper addresses the spectral analysis of cyclostationary (CS) signals from a generic point of view, with the aim to provide the practical conditions of success in a wide range of applications, such as in mechanical vibrations and acoustics. Specifically, it points out the similarities, differences and potential pitfalls associated with cyclic spectral analysis as opposed to classical spectral analysis. It is shown that non-parametric cyclic spectral estimators can all be derived from a general quadratic form, which yields as particular cases "cyclic" versions of the smoothed, averaged, and multitaper periodograms. The performance of these estimators is investigated in detail on the basis of their frequency resolution, cyclic leakage, systematic and stochastic estimation errors. The results are then extended to more advanced spectral quantities such as the cyclic coherence function and the Wigner-Ville spectrum of CS signals. In particular an optimal estimator of the Wigner-Ville spectrum is found, with remarkable properties. Several examples of cyclic spectral analyses, with an emphasis on mechanical systems, are finally presented in order to illustrate the value of such a general treatment for practical applications.
机译：本文从一般的角度讨论了循环平稳（CS）信号的频谱分析，目的是为广泛的应用（例如机械振动和声学）提供成功的实际条件。具体而言，它指出了与经典光谱分析相反的与循环光谱分析相关的相似性，差异和潜在的陷阱。结果表明，非参数循环频谱估计器都可以从一般的二次形式中得出，在特定情况下，可以生成平滑，平均和多锥周期图的“循环”形式。这些估计器的性能将根据其频率分辨率，循环泄漏，系统和随机估计误差进行详细研究。然后将结果扩展到更高级的频谱量，例如CS信号的循环相干函数和Wigner-Ville频谱。尤其是发现了具有明显特性的Wigner-Ville谱的最佳估计器。最后给出了一些循环光谱分析的例子，重点是机械系统，以说明这种一般处理方法在实际应用中的价值。

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