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.

Descripción

Título: General solution of certain matrix equations arising in filter design applications
Autor/es:
  • Domínguez Jiménez, María Elena
Tipo de Documento: Artículo
Título de Revista/Publicación: Linear Algebra and Its Applications
Fecha: Abril 2008
Volumen: 432
Materias:
Palabras Clave Informales: Toeplitz matrices, spectral factorization, paraunitary filters, filter design
Escuela: E.T.S.I. Industriales (UPM)
Departamento: Matemática Aplicada a la Ingeniería Industrial [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

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.

Más información

ID de Registro: 2784
Identificador DC: http://oa.upm.es/2784/
Identificador OAI: oai:oa.upm.es:2784
Identificador DOI: 10.1016/j.laa.2009.09.023
URL Oficial: http://www.elsevier.com/wps/find/journaldescription.cws_home/522483/description#description
Depositado por: Memoria Investigacion
Depositado el: 08 Abr 2010 11:00
Ultima Modificación: 20 Abr 2016 12:26
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