•The Tooth-FFT algorithm is introduced to track time-varying frequency components.•A method to detect incipient and consolidated faults in induction motors is proposed.•The method uses as input the current monitored during the motor start-up transient.•Healthy, incipient and consolidated BRB faults are considered in the experimentation.•A percentage of detection of 97.5% is obtained for all the possible motor conditions. Motor current signals analysis (MCSA) is a widely used approach for fault diagnostics in induction motors (IMs). It consists of detecting a specific signature or pattern associated to a fault condition from current signals. In particular, the fault of broken rotor bars (BRBs) is featured by a V-shaped pattern in the time-frequency domain during the startup transient. Although many techniques and methodologies have been presented in literature, most of them have been focused on analyzing consolidated faults such as one- BRB and multiple BRBs; in contrast, the BRB incipient detection, such as half BRB, has been rarely investigated. Hence, a methodology based on a new technique named Tooth-fast Fourier transform (FFT) to detect both incipient and consolidated BRB conditions is presented in this work. It consists of two windows moving along the analyzed current signal, where the FFT is performed for each window. Next, the spectra are subtracted for minimizing the stationary frequencies and maximizing the moving-ones. The signature of the moving frequencies in the resulting spectrogram has a “teeth” shape, giving the name to the proposed technique. Next, a weight function and a classification stage employing four indicators are presented for automatic diagnostics. The proposal is validated and tested using both synthetic and real signals. For the latter, different levels of BRB, i.e., half BRB, one BRB, and two BRBs, are considered. Results demonstrate the effectiveness and usefulness of the proposal to detect both incipient and consolidated BRB faults in IMs.