Construction of Multiwavelets in Terms of a Novel Transformation
Jianwei Yang · Gongcheng shuxue xuebao · 2005
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.