Resumen de Partial parameterization of orthogonal wavelet matrix filters

Mariantonia Cotronei, Matthias Holschneider

• In this paper we propose a procedure which allows the construction of a large family of FIR d × d matrix wavelet filters by exploiting the one-to-one correspondence between QMF systems and orthogonal operators which commute with the shifts by two. A characterization of the class of filters of full rank type that can be obtained with such procedure is given.

  In particular, we restrict our 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 in the case d = 2 are given, as a result of a local analysis of the parameterization obtained from perturbing the Haar system.