General solution of certain matrix equations arising in filter design applications

Domínguez Jiménez, María Elena (2008). General solution of certain matrix equations arising in filter design applications. "Linear Algebra and Its Applications", v. 432 (n. 8); pp. 2077-2088. ISSN 0024-3795. https://doi.org/10.1016/j.laa.2009.09.023.

Description

Title: General solution of certain matrix equations arising in filter design applications
Author/s:
  • Domínguez Jiménez, María Elena
Item Type: Article
Título de Revista/Publicación: Linear Algebra and Its Applications
Date: April 2008
ISSN: 0024-3795
Volume: 432
Subjects:
Freetext Keywords: Toeplitz matrices, spectral factorization, paraunitary filters, filter design
Faculty: E.T.S.I. Industriales (UPM)
Department: Matemática Aplicada a la Ingeniería Industrial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In this work we present the explicit expression of all rectangular Toeplitz matrices B,C which verify the equation BBH +CCH = aI for some a > 0. This matrix equation arises in some signal processing problems. For instance, it appears when designing the even and odd components of paraunitary filters, which are widely used for signal compression and denoising purposes. We also point out the relationship between the above matrix equation and the polynomial B´ezout equation |B(z)|2 +|C(z)|2 = a > 0 for |z| = 1. By exploiting this fact, our results also yield a constructive method for the parameterization of all solutions B(z),C(z). The main advantage of our approach is that B are C are built without need of spectral factorization. Besides these theoretical advances, in order to illustrate the effectiveness of our approach, some examples of paraunitary filters design are finally given.

More information

Item ID: 2784
DC Identifier: http://oa.upm.es/2784/
OAI Identifier: oai:oa.upm.es:2784
DOI: 10.1016/j.laa.2009.09.023
Official URL: http://www.elsevier.com/wps/find/journaldescription.cws_home/522483/description#description
Deposited by: Memoria Investigacion
Deposited on: 08 Apr 2010 11:00
Last Modified: 20 Apr 2016 12:26
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