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本文从理论上分析了小波变换对被光滑化了的奇异性信号进行处理的效果，证明了小波与高斯函数、小波与任意光滑函数的卷积仍是一个小波．并实际应用于刀具磨损时切削力信号的检测，结果表明可有效地分析刀具的磨损状况．
This paper analyzes the effect of wavelet transform on the smoothed singularity signal theoretically and proves that the wavelet and Gaussian function, the convolution of wavelet and any smooth function is still a wavelet. It is also applied to the detection of cutting force signal when the tool is worn. The results show that the tool wear can be effectively analyzed.