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In the spectrum analyze, noise in the signals measured by spectrum equipment are often unavoidable. Therefore the useful information can not be accurately extracted, which led to the accuracy and precision decline of the analyze results. Mexican Hat de-noising algorithm (MHDA) is an effective method to reduce the noise aiming at the spectrum signals. It selects the Mexican Hat wavelet function and operates with the original signals, which realizes the separation of signals and noise. In this paper, the MHDA is applied to analyze the data of terahertz time-domain spectroscopy (THz-TDS). The simulation results show that it has perfectly de-nosing ability to both low-frequency signals and high-frequency signals and the de-noising effect is improved. Meanwhile, after de-noising, the authors can not only improve the spectral revolution, but also get more spectral information.