基于分数小波变换的空域相关特性的信号降噪新方法

简要介绍了分数小波变换的基本思想及在信号处理方面的特点。利用分数小波变换系数在不同尺度上对应点处的相关性对其进行选择和处理，这样处理后的分数小波变换系数基本上对应着信号的边缘，然后对信号系数进行重构，达到了降噪的目的。以数值仿真和实测齿轮箱振动信号为例，研究了该方法的降噪效果，同时和小波包直接降噪进行了比较。结果表明，该方法能够有效降低振动信号中的背景噪声。

New De noising Method Based on Spatially Correlativity of Fractional Wavelet Transform

The basic theory of fractional wavelet transform (FrWT), including the construction and fast computation of FrWT, and its features in signal processing is introduced at first. FrWT coefficients are processed and selected appropriately based on their relevance in the corresponding points in different scales. The processed FrWT coefficients generally correspond to the signal edge, so that the original signal can be reconstructed and de noised. Compared with the de noising method by traditional wavelet packet transform, the de noising performance of this new method is illustrated through some simulated and measured signals from gear system. At last, the possibility of application of this method is discussed.