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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. 20772088. ISSN 00243795.
Title:  General solution of certain matrix equations arising in filter design applications 

Author/s: 

Item Type:  Article 
Título de Revista/Publicación:  Linear Algebra and Its Applications 
Date:  April 2008 
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 [hasta 2014] 
Creative Commons Licenses:  Recognition  No derivative works  Non commercial 

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Official URL: http://www.elsevier.com/wps/find/journaldescription.cws_home/522483/description#description
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.
Item ID:  2784 

DC Identifier:  http://oa.upm.es/2784/ 
OAI Identifier:  oai:oa.upm.es:2784 
Deposited by:  Memoria Investigacion 
Deposited on:  08 Apr 2010 11:00 
Last Modified:  20 Apr 2016 12:26 