Aeroacoustic signals, as typically returned by recordings of pressure fluctuations generated by rotating machines, often exhibit rich mixtures of tonal and broadband components. The separate analysis of these constituents is important from an engineering point of view, as they relate to different physical mechanisms. This paper is concerned with the extraction of tonal components. The characteristics of aeroacoustic signals can make this task challenging, because tones are numerous, nonharmonically related, and subjected to random modulations. A solution is proposed based on the theory of angle-time cyclostationarity, which seems flexible enough to deal with these constraints. A special effort is made to render the methodology as standalone as possible. This is achieved by automatically setting up the leading parameters with data-driven strategies. The methodology is illustrated on counter-rotating open rotor data that are known to be challenging.