2023-03-23T21:20:40Z
https://oa.upm.es/cgi/oai2
oai:oa.upm.es:2784
2016-04-20T12:26:48Z
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747970653D61727469636C65
General solution of certain matrix equations arising in filter design applications
Domínguez Jiménez, María Elena
Mathematics
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.
E.T.S.I. Industriales (UPM)
https://creativecommons.org/licenses/by-nc-nd/3.0/es/
2008-04
info:eu-repo/semantics/article
Article
Linear Algebra and Its Applications, ISSN 0024-3795, 2008-04, Vol. 432, No. 8
PeerReviewed
application/pdf
eng
http://www.elsevier.com/wps/find/journaldescription.cws_home/522483/description#description
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2009.09.023
https://oa.upm.es/2784/