非均匀子波空间采样定理

Nonuniform Sampling Theorem for Wavelet Space

本文从非均匀采样出发，详细研究了非均匀采样的Ｗａｌｔｅｒ子波空间采样定理的存在条件，给出了Ｓｈａｎｎｏｎ采样定理的一类非均匀采样形式．对紧支尺度函数张成的子波空间，给出了一类非均匀采样方法，使得对该空间中的任意紧支信号，非均匀采样成为可能．文中还指出了非均匀紧支子波空间采样的优点，数值实例验证了理论的正确性．

The condition of nonuniform sampling for Walter＇s sampling theorem and a kind of nonuniform sampling for Shannon sampling theorem are given in this paper. For the signal space spanned by compactly supported scaling function, nonuniform sampling theorem, which makes it possible to sample arbitrary compactly supported signal in the space is presented. Moreover,the advantages of nonuniform sampling for compactly supported wavelet space are given. In the end,the numerical examples show that theory presented in this paper is correct.