Cyclic spectral analysis in practice

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.