This work offers a reliable solution to the detection of broken rotor bars in induction machines with a novel methodology, which is based on the fact that the fault related harmonics will have oscillating amplitudes due to the speed ripple effect. The method consists of two main steps: initially, a time-frequency transformation is used and the focus is given on the steady-state regime; thereupon, the fault related frequencies are handled as periodical signals over time and the classical Fast Fourier Transform is used for the evaluation of their own spectral content. This leads to the discrimination of sub-components related to the fault and to the evaluation of their amplitudes. The versatility of the proposed method relies on the fact that it reveals the aforementioned signatures to detect the fault, regardless of the spatial location of the broken rotor bars. Extensive finite element simulations on a 1.1 MW induction motor and experimental testing on a 1.1 kW induction motor lead to the conclusion that, the method can be generalized on any type of induction motor independently from the size, power, number of poles and rotor slot numbers.