Mechanical transmission is widely used in vehicles,machine tools,construction machinery and other engineering fields,the study of mechanical transmission reliability,damage mechanism,fault diagnosis and signal processing method has great significance and value.The traditional signal processing algorithms,such as FFT algorithm,the fast Fourier transform algorithm,since its fast speed,stable spectrum analysis,has been widely used in engineering. But the signals of engineering practice are very complex,nonlinear,and non-stationary,Within the external noise interference coupled,makes the analysis and processing more difficult,which lead to the spectral analysis based on FFT method has been very limited. For the advantages of computation speed,features and stability of FFT algorithm,the secondary FFT,third FFT algorithm,n-FFT algorithm（ 2 npoints less than the signal sample points） were discussed in theory and research,the theory was explored and verified by experiment signals. It was applied in the classification study of gear signal. Analysis shows that n-FFT algorithm is fast,with high feature accumulation,is beneficial to the classify and fault monitoring and diagnosis of gear operating state.