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The aim of this paper is to propose a comparative study between three advanced signal processing methods for the vibratory diagnosis of rotating machines working in industrial conditions. Cyclostationary analysis, empirical mode decomposition (EMD), and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) are then applied for the detection of mechanical defects of a turbofan machine in the biggest fertilizer company in Algeria. These methods proved their efficiency for the diagnosis of specific defects, like rolling bearing and gear defects in laboratory test rigs, but their application in industrial field remains limited. The application of these methods on vibratory signals measured in low, medium, and high-frequency range allowed determining the efficiency of each method to diagnose the occurrence of different defects manifested in the three considered frequency ranges. The great advantage of the modulation intensity distribution (MID), and its integration (IMID), obtained from the cyclostationary analysis, is proven compared to the envelope spectra performed from the EMD or the CEEMDAN approaches, especially for defects inducing modulation phenomena. Finally, the main result of this paper is that the advanced signal processing tools can be easily applied on signals measured in industrial environment, and can be extended to detect mechanical defects in real running conditions, more real than those simulated on laboratory test rigs. [ABSTRACT FROM AUTHOR]