Abstract: The time-frequency domain characteristics of acoustic emission signal and its essential relationship with mechanical properties of coal are the basis for predicting and warning the instability of coal. On the basis of acoustic emission monitoring test for the compressive failure of coal with different gangues and original cracks,the time-fre- quency domain evolution of acoustic emission signal is discussed in detail combined with digital signal theory,rock me- chanics and other related approaches,and the wavelet transform method is introduced. The mechanical expression of amplitude and frequency of stress wave is established,which is induced by elastic energy released from crack growth. The results showed that with the increase of weak gangue or crack in coal,its strength and elastic modulus decrease, the softening characteristic is obvious in the post-peak phase,and there is a signal surge point which transforms from a low amplitude oscillation to a high amplitude pulse of acoustic emission. The higher strength of coal,the higher the am- plitude of energy signal,the more cumulative total energy,the larger amplitude of waveform,the longer interval between the two adjacent peaks of signal waveform,and the fewer small oscillations mixed in the signal. The wavelet basis func- tions of db5 and sym2 have the highest similarity with the time-domain waveforms of the surge point and peak point re- spectively,which is more suitable for the study of acoustic emission signals of coal. The main frequency band of signal is 0-70 kHz,the lower loading stress level,the wider the signal frequency distribution,the signal band distribution gradually moves to the main frequency with the stress increase. The variation range of stress wave amplitude is deter- mined by elastic modulus and crack propagation rate,the crack size determines the variation trend of amplitude and frequency,crack propagation rate is a key parameter to determine the stress wave frequency,then three parameters af- fect the time-frequency characteristics of acoustic emission signals. The experimental results establish the qualitative description of crack characterization parameters with the frequency and amplitude of AE signal,which provides a theo- retical basis for improving the accuracy of AE monitoring method. Therefore,the quantitative application of the theory is the focus for the future research.