无显式表达小波在不同尺度下的离散生成算法及幅频特性  

Discrete generation algorithm and amplitude-frequency property of wavelet without analytic expression in various scales

作　　者：赵学智[1] 叶邦彦[1] 陈统坚[1] ZHAO Xue—zhi;YE Bang—yan;CHEN Tong-jian(School of Mechanical and Automotive Engineering,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]华南理工大学机械与汽车工程学院,广东广州510640

出　　处：《振动工程学报》2011年第5期546-554,共9页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(50875086,50305005);广州市科技计划资助项目(2008J1-C101)

摘　　要：为了获得无显式表达小波在不同尺度上的幅频特性,必须先解决它在时域各尺度上的离散生成。分析了原有的一个生成算法存在的问题,进而基于多分辨分析理论,提出了一种新的离散生成算法,利用小波低通滤波器系数通过迭代可得到不同尺度上的尺度和小波函数,由此研究了Daubechies2~10号小波在5个尺度上的幅频特性,得到的结果直观地显示了此类小波在不同尺度间存在较大频带重叠,其中D2~D4号小波的频带从第3个尺度开始还存在旁瓣,但在D9~D10号小波中旁瓣基本消失,频带重叠程度也相对减少。通过信号处理实例证实了这种幅频特性的准确性。To get the amplitude-frequency property of wavelet without analytic expression in the various scales,the discrete generation of wavelet in these scales in time domain should be solved firstly.The defect of one previous generation algorithm being pointed out and analyzed,a new algorithm is proposed based on multiresolution analysis theory,and the scale and wavelet functions in the various scales can be got by this new one using wavelet low pass filter coefficients.The amplitude-frequency property of No.2~10 Daubechies wavelets in the 5 scales is obtained by this algorithm,the results show directly that for these wavelets there are big overlaps among their frequency bands of the various scales,and furthermore for No.2-4 Daubechies wavelets there are some side segments in their frequency bands beginning from the third scale,while for No.9-10 Daubechies wavelets,the side segments disappear and their frequency overlap will also be certain reduced.Signal processing examples are presented to verify the accuracy of this kind of amplitude-frequency property.

关 键 词：小波分析 小波函数 尺度函数 离散生成 幅频特性 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]