恒等逼近与连续小波变换的点态逼近  

Approximate identities and the pointwise approximation of continuous wavelet transform

作　　者：宋丛威[1] 邸继征[1] 

机构地区：[1]浙江工业大学理学院,浙江杭州310032

出　　处：《浙江工业大学学报》2011年第6期693-698,共6页Journal of Zhejiang University of Technology

摘　　要：类似于Fourier变换,连续小波变换的反演公式与卷积的恒等逼近也存在着密切联系.实际上,可以将连续小波变换看作是一种逼近单位的构造方法.前人已经对小波变换的点态逼近做过了充分的讨论,但都没有与恒等逼近相联系.利用恒等逼近证明了几个新的连续小波变换的点态逼近定理,并在此基础上给出了在不同条件下逼近的误差估计,为信号去噪提供了理论依据.最后的数值实验成功地进完成了信号去噪,从而验证了这些定理的正确性和相关算法的可用性.Like Fourier transform, there is an intimate relationship between the inverse formula of continuous wavelet transform and the approximate identities of convolution. At fact, continuous wavelet transform could be regarded as a constructing method of the approximate identifies. The pointwise approximation of wavelet transform had been fully discussed previously, but was not associated with the approximate identities. This paper proves several new theorems about the pointwise approximation of continuous wavelet transform with approximate identities. Based on these theorems, the error estimates of the approximating under different conditions are given. It provides the theoretical basis for signal denoising. Finally, the numerical experiment shows that the signal noise can be removed successfully, the correctness of the theorems and usability of the relevant algorithm are verified.

关 键 词：连续小波变换 恒等逼近 点态逼近 FOURIER变换 

分 类 号：O174.21[理学—数学]