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Motor current signature analysis (MCSA) is the reference method for the diagnosis of medium-large machines in industrial applications. However, MCSA is still an open research topic, as some signatures may be created by different phenomena, wherein it may become sensitive to load and inertia variations, and with respect to an oscillating load torque, although suitable data normalization can be applied. Recently, the topic of diagnostic techniques for drives and low to medium size machines is becoming attractive, as the procedure can be embedded in the drive at no additional thanks to a dedicated firmware, provided that a suitable computational cost is available. In this paper, statistical time-domain techniques are used to track grid frequency and machine slip. In this way, either a lower computational cost or a higher accuracy than traditional discrete Fourier transform techniques can be obtained. Then, the knowledge of both grid frequency and machine slip is used to tune the parameters of the zoom fast Fourier transform algorithm that either increases the frequency resolution, keeping constant the computational cost, or reduces the computational cost, keeping constant the frequency resolution. The proposed technique is validated for rotor faults.