In this work, we present a diagnosis system for rolling bearings that leverages simultaneous measurements of vibrations and machine rotation speed. Our approach combines the robustness of simple time domain methods for fault detection with the potential of machine learning techniques for fault location. This research is based on a neural network classifier, which exploits a simple and novel preprocessing algorithm specifically designed for minimizing the dependency of the classifier performance on the machine working conditions, on the bearing model and on the acquisition system set-up. The overall diagnosis system is based on light algorithms with reduced complexity and hardware resource demand and is designed to be deployed in embedded electronics. The fault diagnosis system was trained using emulated data, exploiting an ad-hoc test bench thus avoiding the problem of generating enough data, achieving an overall classifier accuracy larger than 98%. Its noteworthy ability to generalize was proven by using data emulating different working conditions and acquisition set-ups and noise levels, obtaining in all the cases accuracies greater than 97%, thereby proving in this way that the proposed system can be applied in a wide spectrum of different applications. Finally, real data from an on-line database containing vibration signals obtained in a completely different scenario are used to demonstrate the distinctive capability of the proposed system to generalize.