一种有效的小波紧框架设计

利用 W.Swelden 和 M.J.Shensa 关于插值性的刻画，证明了不存在具有3个生成元且满足插值性的小波紧框架．在满足近似插值性及较高阶消失矩的性质下，设计一个低通滤波器，利用不等式得到3个滤波器，从而得到小波紧框架．所得的高通滤波器中有一个满足对称性，一个满足反对称性．设计所得到的滤波器都含有一个自由参数，此参数的引入增加了小波框架的选择余地．

An efficient way for wavelet tight frames construction

Using the demonstration about the interpolation of W. Swelden and M. J. Shensa , we prove that the interpolated wavelet tight frame generated by three generators does not exist. Under satisfying nearly interpolation and higher vanishing moment, we design a low-pass filter, and then using an inequality giving by Ron, we will get three high-pass filters. Therefore we can get the wavelet tight frames that satisfy our properties. Two of those high-pass filters satisfy symmetry or antisymmetry, and all of them have a free parameter. The greater freedom will widen the selection of both low-pass and high-pass filters. Finally, we give the algorithm for filters and some concrete examples of wavelet tight frames.