二元小波矩阵扩充的逆问题

An Inverse Problem on Matrix Extension of Bivariate Wavelets

本文我们研究了二维小波构造中所需的矩阵扩充问题，结论如下：对次数不超过三的低通滤波器，能扩充为酉矩阵（公式1．9）当且仅当该滤波器具有形式（公式3．1）

An inverse problem on matrix extension is studied in order to investigate the construction of bivariate wavelets. The main result can be stated as follows: suppose that m is a low-pass filter, then it can be extended to a unitary matrix (1.9) if it and only if it has the form of (3.1).