Fault diagnosis of rotor asymmetries in induction machines working at a very low slip, through Fourier-based methods, usually requires a long acquisition time to achieve a high spectral resolution and a high sampling frequency to reduce aliasing effects. However, this approach generates a huge amount of data, which makes its implementation difficult using embedded devices with small internal memory, such as digital signal processors and field programmable gate arrays or devices with low computing power. In this paper, a new simplified diagnostic signal designated as the reduced envelope of the stator current is introduced to address this problem. The reduced envelope signal is built using only one sample of the current per cycle without any further processing, and it is demonstrated that it carries the same spectral information about the fault as the full-length current signal. Based on this approach, an embedded device has only to store and process a minimal set of samples compared with the raw current signal for a desired resolution. In this paper, the theoretical basis of the proposed method is presented, as well as its experimental validation using two different motors with broken bars: 1) a high-power induction motor working in a factory; and 2) a low-power induction motor mounted in a laboratory test bed.