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In order to predict the rock rupture and instability, acoustic emission signals of natural sandstones and hydrous sandstones are analyzed through the Fast Fourier Transform and the Welch method. It is found that the acoustic emission signals of the hydrous sandstones have narrower range of frequency spectrum and lower average dominant frequencies than the natural sandstones. The dominant frequencies of the acoustic emission signals of the hydrous sandstones reduce more dramatically. In addition, two types of Welch power spectrum of the acoustic emission signals in terms of the shape are presented in this paper, which are named Type A and Type B. The Type B Welch power spectrum emerges when the acoustic emission occurs frequently, in which a disaster tends to appear. Time baselines are selected when relative stronger cracks and crack coalescence happens. We find that the greater signals energy at the time baseline, the higher probability of occurrence of Type B spectrum appears before the time baseline. Also, the probabilities of Type B before the corresponding the baseline time of rock last rupture in hydrous sandstones are higher than that of natural sandstones.