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.

Partial parameterization of orthogonal wavelet matrix filters / Cotronei, Mariantonia; Holschneider, M. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - 243:(2013), pp. 113-125. [10.1016/j.cam.2012.11.016]

Partial parameterization of orthogonal wavelet matrix filters

COTRONEI, Mariantonia
;
2013-01-01

Abstract

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.
2013
Full rank matrix filters; Multichannel wavelets; Quadrature Mirror Filters
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/6600
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