MRA超小波的一种判定

A characterition of MRA super-wavelets

超小波是小波分析中一种特殊的信号分析方法.从讨论超小波分量的角度出发,论证了直和希尔伯特空间L2(R)(m)=sum from j=1 to m  L2(R)中超小波是MRA超小波的充分必要条件.即一个超小波是MRA结构当且仅当每个特殊线性子空间的维数是0或者1.

The super-wavelets is a special signal analysis method in wavelet analysis. From the angle that dicussing the component of super-wavelets, we developed a theory of the MRA super-wavelets, which is necessary and sufficient conditions of super-wavelets arises from MRA construction. It is shown that a super-wavelet arises from our MRA construction if and only if the dimension of each particular linear space is either zero or one.