二维Parseval小波框架包的性质

摘要

当加细方程中伸缩因子为常正整数时,研究了由酉拓展原理构造的一类二维Parseval小波框架包的性质.运用时频分析方法,建立了二维基本小波框架包与对应的滤波器组的关系式.给出了二维基本小波框架包构成空间L2(R2)中Parseval小波框架的充分条件,进而,由二维Parseval小波框架包构造了空间L2(R2)直交分解子空间.%The properties of a class of two-dimensional Parseval wavelet-framed packets constructed with unitary expansion principle, is investigated as the dilation factor in the refinement equation is a fixed positive integer.The dependence of two-dimensional basic wavelet-framed packets on their corresponding filter bank is established by using time-frequency analysis method.A sufficient condition for availability of Parseval wavelet frame in two-dimensional basic wavelet-framed packets-constituted space L2(R2) and further, the orthogonal decomposition subspaces in space L2(R2) are constituted with the two-dimensional basic Parseval wavelet-framed packets.