This research deals with the discrimination between conditions of faults in rolling element bearings based on a global spectral analysis. This global spectral analysis allows to obtain spectral features with significant discriminatory power. These features are extracted from the envelope spectra of vibration signals without prior knowledge of the bearings specific parameters and the characteristic frequencies. These extracted spectral features will then be the global spectral signature produced by the bearing faults. Since the signature produced by the faults in bearing balls is very weak, and hard to be detected and identified, this paper proposes the linear discriminant analysis as part of the global spectral analysis method in order to improve the diagnosis of ball faults. The application on experimental vibration data acquired from bearings containing different types of faults with different small sizes shows the proficiency of the overall method. The Bhattacharyya distance is used to confirm the efficiency of the obtained results.