【摘要】 该文研究对应于 3-带尺度函数的小波紧框架 ,这个小波紧框架是由 V1中的 l个函数 ψ1,ψ2 ,… ,ψl构成 .首先给出这 l个函数构成小波紧框架的充分条件 .由此给出由 3-带尺度函数构造出一个小波紧框架的显式公式 .特别的 ,如果给定尺度函数的符号是有理函数 ,则可以构造出符号为有理函数的小波紧框架 .最后还给出类似于小波的小波紧框架的分解与重构算法更多还原

【Abstract】 This paper studies wavelet tight frames associated with given scaling functions with dilation factor 3. The wavelet frames consist of finite number of functions ψ\+1, ψ\+2,\:, ψ\+n ∈V\-1. First present sufficient conditions for existence of wavelet tight frames generated by the \$l\$ functions and then give explicit structure formula of wavelet tight frames. In particular, if masks of the scaling functions are rational functions, then the corresponding wavelet frame with rational masks can be found. Finally, the authors can derive the decomposition and reconstruction formulas which are similar to those of orthonormal wavelets.更多还原