摘要
讨论了框架与规范正交基之间的关系,并给出了从小波框架出发构造小波基的一般方法.作为该方法的应用实例,构造出一组规范正交小波基,并证明了其规范正交性.这组小波基的最大特点是其伸缩因子a0等于3,它不仅规范正交,而且时频局部化相对较好,与著名的Meyer小波相比,它在频域内支集较小,在时域内衰减较快.该小波函数在时域和频域内均有一定的对称性.
The relation between frames and orthonormal bases is discussed and a new method for constructing the wavelet basis based on the wavelet frame is also presented. An orthonormal wavelet basis is constructed as an example and the proof of its orthonormality is given. Such a wavelet basis is characterized by its dilation factor a 0= 3. It has relatively good time frequency localization as well as is orthonormal. Compared with the famous Meyer wavelet, it has a smaller support in time and decays faster in frequency. Additionally, this wavelet has some symmetry in both time and frequency.
出处
《西安电子科技大学学报》
EI
CAS
CSCD
北大核心
2000年第1期49-51,57,共4页
Journal of Xidian University
基金
军事电子预研基金资助项目 !(G970 8C0 2 )
关键词
紧框架
小波
规范正交基
tight frame
wavelet
orthonormal basis
