Abstract: In many mechanical components, cylindrical structures are often subjected to alternating stress conditions, making them susceptible to fatigue cracks, ultimately leading to material failure and accidents. Nonlinear ultrasound can characterize the damage degree of fatigue cracks through a nonlinear coefficient, accurately extracting the fundamental frequency and second harmonic from the signal is crucial. This paper proposed a time-frequency signal processing method based on wavelet transform to extract the fundamental frequency and second harmonic signals. Firstly, the quantitative relationship between the nonlinear coefficients obtained by wavelet transform processing on various wavelet bases and the degree of fatigue crack damage was analyzed. Secondly, the simulation was used to obtain the nonlinear ultrasonic guided wave signal in the circular tube with fatigue cracks, and the nonlinear coefficients calculated by other time-frequency analysis methods were compared. Finally, a quantitative relationship between the fatigue crack damage degree and the nonlinear coefficients obtained by various methods was established, proving that the nonlinear coefficients calculated by the proposed method can better characterize the fatigue crack damage degree.