In previous articles, both the procedure and the advantages of the use of advanced mathematical tools,(as for example the Discrete Wavelet Transforms (DWT) and the continuous wavelet transforms (CWT)), for the time-frequency analysis of current signals captured in the stator during transients of starting and stopping have been deeply justified. The purpose of this analysis is the detection of rotor asymmetries as well as of possible eccentricities in induction motors. This article aims to analyze, from a qualitative point of view, the influence of the starting system on the results of the diagnosis method based on the analysis of the start-up current by using the DWT. Likewise, emphasis made on the impact and influence in the Wavelet Analysis (either through DWT or CWT) of harmonics introduced by the network, the motor itself and the possible fluctuations in the load torque. The results demonstrate the validity of the method, which presents a great robustness, regardless of the starting method or operating conditions. The theoretical conclusions were supported by actual measurements obtained in laboratory motors.