The diagnosis of induction motors through the spectral analysis of the stator current allows for the online identification of different types of faults. One of the major difficulties of this method is the strong influence of the mains component of the current, whose leakage can hide fault harmonics, especially when the machine is working at very low slip. In this paper, a new method for demodulating the stator current prior to its spectral analysis is proposed, using the Teager-Kaiser energy operator. This method is able to remove the mains component of the current with an extremely low usage of computer resources, because it operates just on three consecutive samples of the current. Besides, this operator is also capable of increasing the signal-to-noise ratio of the spectrum, sharpening the spectral peaks that reveal the presence of the faults. The proposed method has been deployed to a PC-based offline diagnosis system and tested on commercial induction motors with broken bars, mixed eccentricity, and single-point bearing faults. The diagnostic results are compared with those obtained through the conventional motor current signature analysis method.