Current spectrum analysis is a proven technique for fault diagnosis in electrical machines. Current spectral estimation is usually performed using classical techniques such as periodogram (FFT) or its extensions. However, these techniques have several drawbacks since their frequency resolution is limited and additional post-processing algorithms are required to extract a relevant fault detection criterion. Therefore, this paper proposes a new parametric spectral estimator that fully exploits the faults sensitive frequencies. The proposed technique is based on the maximum likelihood estimator and offers high-resolution capabilities. Based on this approach, a fault criterion is derived for detecting several fault types. The proposed faults detection technique is assessed using simulations, issued from a coupled electromagnetic circuits approach-based simulation tool. It is afterwards validated using experiments on a 0.75-kW induction machine test bed for the particular case of bearing faults.