Partial parameterization of orthogonal wavelet matrix filters

In this paper we propose a procedure which allows the construction of a largefamily of FIR d x d matrix wavelet filters by exploiting the one-to-one correspondencebetween QMF systems and orthogonal operators which commute with the shifts by two. A characterization of the class of filters of full rank typethat can be obtained with such procedure is given. In particular, we restrictour attention to a special construction based on the representation of SO(2d)in terms of the elements of its Lie algebra. Explicit expressions for the filters inthe case d = 2 are given, as a result of a local analysis of the parameterizationobtained from perturbing the Haar system.