The early detection of gear faults remains a major problem, especially when the gears aresubjected to non stationary phenomena due to defects. In industrial applications, thecrack of tooth is a default very difficult to detect whether using the time descriptors orthe frequency analysis. In this work and based on a numerical model, we prove that thecrack default affects directly the phase of the frequency component of the defective wheel(frequency modulation). To properly estimate the phases, we suggest two high-resolutiontechniques (Estimation of Signal Parameters via Rotational Invariance Techniques ESPRITwith a sliding window and Weighted Least Squares Estimator WLSE). The results of bothmethods are compared to the phase obtained by Hilbert transform. The three techniques arethen applied on a multiplicative signal with a frequency modulation to show the influenceof the amplitude modulation on the quality of phase estimation. We note that the ESPRITmethod is much better in the estimation of frequencies while WLSE shows much efficiency inthe estimation of phases if we keep the frequencies almost stables.