To explore the failure precursors of hard rock, a series of triaxial loading and unloading experiments were carried out on sandstone sample using the acoustic emission systems. The extreme-point symmetric mode decomposition method (ESMD method) was used to denoise and reconstruct the AE data. The AE quiet period in Scheme I becomes much more obvious with the confining pressure increasing, which can be regarded as the precursor information of the sample failure under conventional triaxial compression. Unlike Scheme I, there are no obvious precursory characteristics before failure in Schemes II and III, and the count rate reaches the maximum at the peak point. When the stress ratio ranges from 0.8 to 1.0, the fractal values of acoustic emission can be used to investigate the failure precursors of samples at a lower confining pressure. When the time ratio is greater than 0.8 under higher confining pressures, the fractal values of sandstone samples under unloading paths are rapidly reduced, which can be used to predict rock failure at higher confining pressures.