内积型和卷积型小波变换对信号处理效果的研究

RESEARCH ON SIGNAL PROCESSING EFFECT OF BOTH INNER PRODUCT TYPE OF WAVELET TRANSFORMATION AND CONVOLUTION TYPE OF WAVELET TRANSFORMATION

内积型和卷积型小波变换是小波变换的两种定义形式,由于其迭代算法不同,因而对同一信号有不同的处理效果。以对一个轴承振动信号的处理为例,详细分析了这两种小波变换形式的频带分离效果和对信号中故障特征的提取效果,结果表明,卷积型小波变换对信号的处理效果要优于内积型,不仅其频带分离效果比内积型优越,而且它所提取的故障特征信息也比内积型小波变换要明显得多。最后对比较结果从理论上给予了解释。

The inner product type and convolution type of wavelet transformation are wavelet transformation's two different modality and they have different processing effect for the same signal because their operational algorithm is different. In order to compare the frequency band separating effect and fault extraction effect of these two kinds of wavelet transformation, a bearing's vibrating signal is processed by them respectively and their processing results in every scale are compared in detail. The analyzing results show that signal processing effect of convolution type of wavelet transformation has the advantage of that of inner product type one. Not only has it better frequency band separating effect, but also its ability to extract fault information is superior to that of inner product type of wavelet transformation. At last the theoretic analysis for this phenomenon is given.