基于一种特殊变换的多小波构造(英文)

Construction of Multiwavelets in Terms of a Novel Transformation

本文引入一种矩阵滤波器的特殊变换。任一紧支撑正交多尺度函数都可由一个简单的矩阵滤波器通过这种变换得到。由此给出一种由多尺度函数构造相应紧支撑正交多小波的算法。与传统方法相比,这种方法既不需要对罗朗多项式矩阵逐行降次,也不需要将多项矩阵分解成特殊的形式,并且不受滤波器长度的限制。可以利用该方法构造出GHM正交多小波。

A novel transformation of matrix filter is introduced in this paper. In terms of this type of transformation, any compactly supported orthogonal multiscaling functions can be constructed from a simple matrix conjugate quadrature filter (CQF). As a result, an algorithm is presented for constructing compactly supported orthogonal multiwavelets from the associated multiscaling function. In comparison with the traditional methods, the order of some polynomial matrices need not be decreased row by row and the polyphase matrix need not be factorized into a special form. Furthermore, this method is not restricted by the length of the filter. By this method, the GHM multiwavelets can be derived.