冗余小波变换零相位分解实现方法及应用研究

Zero Phase Decomposition of Undecimated Discrete Wavelet Transform and Its Application

为消除正交小波非对称性引起的非线性相位对分解结果的不利影响,结合零相位滤波原理与冗余小波变换,提出了一类具有零相位特性的冗余小波分解算法——零相位冗余小波变换。该小波变换不仅克服了Mallat算法中隔点采样环节造成的平移可变与频率折叠等诸多缺陷,也消除了传统冗余小波变换分解结果出现移位与畸变的不足,非常适合于微弱特征提取。通过实例分析证明了该算法用于轴承微弱故障特征提取的有效性与优势所在。

In order to eliminate the influence of the non-linear phase resulted from the non-symmetry of orthogonal wavelet on decomposition result,on the basis of zero phase filtering principle and the Undecimated Discrete Wavelet Transform(UDWT),we proposed a UDWT decomposition algorithm with zero phase characteristics,called Zero Phase UDWT(ZPUDWT).The new method can not only overcome the defects of Mallat algorithm,such as overlap of frequency and shift variance,which are caused by down sampling,but also eliminate the displacement and distortion phenomenon in decomposition results of conventional wavelet transform.Therefore,ZPUDWT is very suitable for weak feature extraction.Analysis of an example for weak feature extraction of bearings proved the effectiveness and advantages of the new method.