In the context of automatic and preventive condition monitoring of rotating machines, this paper revisits the demodulation process essential for detecting and localizing cracks in gears and bearings. The objective of the paper is to evaluate the performance of the well-known Hilbert demodulation by providing a quantified assessment in terms of signal processing. For this purpose, vibration test signals are simulated guided by the analysis of real-world measurements. The database comes from a natural wear experimentation on a test bench at an industrial scale and without any fault initiation. In the proposed simulated model, the amplitude modulation is designed in a physical approach in order to be able to set up the number of faulty teeth and their location. The impact of a limited spectral bandwidth filtering is quantified not only for the amplitude but also for the phase modulation estimations. The interactions between the amplitude and phase estimations are discussed. A focus is made on the analytic signal ambiguity due to the non-uniqueness of the amplitude estimation. This property induces an original investigation when demodulating the residual generated after a time synchronous averaging. Finally, as the objective is a continuous surveillance of a machine, results are given for a sequence of real-world measurements in order to visualize the fault evolution through the demodulation process.