The success of vibration-based health monitoring of machines relies on correctly modelling the signals that the machines produce. Over the years, the theory of cyclostationary processes sets a valuable framework provided that machines operate at constant regime. When operating under nonstationary conditions, such as varying speed or load, machine signals are no longer cyclostationary, because they depend on characteristics both scheduled in time and angle. The authors have recently extended the standard cyclostationary framework to angle-time cyclostationary processes which can well model signals, which have spectral characteristics constant in time and, at the same time, statistical properties which exhibit periodicities in angle. The aim of the paper is to contribute to the theoretical foundations of angle-time cyclostationarity. First, a formal definition of angle-time cyclostationary processes is proposed, which is more precise than its former formulation. This is illustrated with some theoretical examples of angle-time cyclostationary processes, which may serve as models for machine vibration signals. Next, the question of estimating the angle-time autocorrelation, a central descriptor of angle-time cyclostationary processes, is addressed in details.
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