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In this paper, a new induction motor diagnosis methodology is proposed. The approach is based on obtaining a 2-D time-frequency plot representing the time-frequency evolution of the main components in an electrical machine transient current. The identification of characteristic patterns in the time-frequency plane caused by many of the fault-related components enables a reliable machine diagnosis. Unlike other continuous-wavelet-transform-based methods, this work uses frequency B-spline (FBS) wavelets. It is shown that these wavelets enable an efficient filtering in the region neighboring the main frequency, as well as enable a high level of detail in the time-frequency maps. As a consequence, the evolution of the most important current components is precisely traced. These characteristics make it easy to identify the patterns related to the fault components. The technique is applied to the experimental no-load start-up current of motors in a healthy state and with broken bars; the FBS capabilities are revealed. One of the novelties of this paper is the fact that the diagnosis is carried out via the identification not only of the traditional lower sideband harmonic but also of the upper sideband harmonic and four additional fault-related components.