Mechanical Systems and Signal Processing Mechanical Systems and Signal Processing 21 (2007) 597–630 Cyclic spectral analysis in practice Je´roˆme Antoni à Laboratory Roberval of Mechanics, University of Technology of Compie`gne, 60205 Compie`gne, Cedex, France Received 29 November 2005; received in revised form 22 August 2006; accepted 23 August 2006 Abstract 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. r 2006 Elsevier Ltd. All rights reserved. Keywords: Cyclic spectral analysis; Cyclostationary signals; Cyclic spectrum; Spectral correlation; Cyclic coherence function; Wigner–Ville spectrum; Cyclic leakage 1. Introduction 1.1. Objectives During the last two decades, the theory of cyclostationarity has emerged as a new approach for characterising a certain type of nonstationary signals. It has recently lead to a number of technological breakthroughs essentially in the field of communication and similar advances are likely to arrive shortly in other engineering fields. One major property of cyclostationary (CS) signals is that they can be easily separated from other interfering signals even in the case of overlapping spectral supports. This allows new possibilities to detect, identify, characterise, and handle signals hidden in high levels of stationary noise. Surprisingly, such potentials have remained virtually unknown from engineers and scientists in vibrations and acoustics— notwithstanding some isolated precursory works on the subject—despite the fact that cyclostationarity ARTICLE IN PRESS www.elsevier.com/locate/jnlabr/ymssp 0888-3270/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2006.08.007 à Tel.: +33 3 44 23 45 25; fax: +33 3 44 23 44 77. E-mail address: antoni@utc.fr.