最小不对称高密度小波基的构造及应用

Construction of least asymmetric higher density wavelet bases and its application

具有2个生成元的高密度离散小波变换能实现间尺度分析,并具有近似平移不变性,因而很适合于信号降噪。针对现有高密度小波基对称性较差的问题,提出一种构造最小不对称高密度小波基的方法。该法通过在最大扁平线性相位FIR滤波器的所有可能因式分解结果中进行最优化选择,得到相位最接近线性的低通滤波器,进而求出2个小波滤波器,然后便能构造出最小不对称高密度小波。仿真试验表明,与原有小波相比,采用新小波可提高高密度离散小波变换的降噪性能。在滚动轴承故障振动信号降噪中的应用结果表明所构造的小波能有效地提取轴承故障特征。

The higher density discrete wavelet transformation with two generators can realize intermediate scales analysis,and is an approximate shift invariant,so that it is very suitable for signal denoising.Aiming at the bad symmetry of the current higher density wavelet bases,an approach for construction of least asymmetric higher density wavelet bases was proposed.The nearest linear-phase low-pass filter was chosen optimally from all the possible factorization results of the maximaum flat linear-phase(FIR)filter with the proposed method.Subsequently,the two wavelet filters were obtained.Then,the least asymmetric higher density wavelets could be constructed.Simulation experiments showed that using the new wavelets can improve the denoising performance of the higher density discrete wavelet transformation compared with the current wavelets.The application results in denoising a roller bearing fault vibration signal showed that the constructed wavelets can effectively extract the bearing fault characteristic from that signal.