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Motor-current-signature analysis has been successfully used in induction machines for fault diagnosis. The method, however, does not always achieve good results when the speed or the load torque is not constant, because this causes variations on the motor-slip and fast Fourier transform problems appear due to a nonstationary signal. This paper proposes a new method for motor fault detection, which analyzes the spectrogram based on a short-time Fourier transform and a further combination of wavelet and power-spectral-density (PSD) techniques, which consume a smaller amount of processing power. The proposed algorithms have been applied to detect broken rotor bars as well as shorted turns. Besides, a merit factor based on PSD is introduced as a novel approach for condition monitoring, and a further implementation of the algorithm is proposed. Theoretical development and experimental results are provided to support the research.