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International audience; Nowadays, the vibration analysis of rotating machine signals is a well-established methodology, rooted on powerful tools offered, in particular, by the theory of cyclostationary (CS) processes. Among them, the squared envelope spectrum (SES) is probably the most popular to detect random CS components which are typical symptoms, for instance, of rolling element bearing faults. Recent researches are shifted towards the extension of existing CS tools – originally devised in constant speed conditions – to the case of variable speed conditions. Many of these works combine the SES with computed order tracking after some preprocessing steps. The principal object of this paper is to organize these dispersed researches into a structured comprehensive framework. Three original features are furnished. First, a model of rotating machine signals is introduced which sheds light on the various components to be expected in the SES. Second, a critical comparison is made of three sophisticated methods, namely, the improved synchronous average, the cepstrum prewhitening, and the generalized synchronous average, used for suppressing the deterministic part. Also, a general envelope enhancement methodology which combines the latter two techniques with a time-domain filtering operation is revisited. All theoretical findings are experimentally validated on simulated and real-world vibration signals.