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Time-frequency analysis of the transient current in induction motors (IMs) is the basis of the transient motor current signature analysis diagnosis method. IM faults can be accurately identified by detecting the characteristic pattern that each type of fault produces in the time-frequency plane during a speed transient. Diverse transforms have been proposed to generate a 2-D time-frequency representation of the current, such as the short time Fourier transform (FT), the wavelet transform, or the Wigner-Ville distribution. However, a fine tuning of their parameters is needed in order to obtain a high-resolution image of the fault in the time-frequency domain, and they also require a much higher processing effort than traditional diagnosis techniques, such as the FT. The new method proposed in this paper addresses both problems using the Gabor analysis of the current via the chirp z-transform, which can be easily adapted to generate high-resolution time-frequency stamps of different types of faults. In this paper, it is used to diagnose broken bars and mixed eccentricity faults of an IM using the current during a startup transient. This new approach is theoretically introduced and experimentally validated with a 1.1-kW commercial motor in faulty and healthy conditions.