LMI characterization for the convex hull of trigonometric curves and applications

Tuan, HD; Son, TT; Vo, B; Nguyen, TQ

LMI characterization for the convex hull of trigonometric curves and applications

Tuan, HD

Son, TT Vo, B Nguyen, TQ

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Publication Type:: Conference Proceeding
Citation:: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 2005, IV
Issue Date:: 2005-01-01

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Field	Value	Language
dc.contributor.author	Tuan, HD https://orcid.org/0000-0003-0292-6061	en_US
dc.contributor.author	Son, TT	en_US
dc.contributor.author	Vo, B	en_US
dc.contributor.author	Nguyen, TQ	en_US
dc.date.issued	2005-01-01	en_US
dc.identifier.citation	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 2005, IV	en_US
dc.identifier.isbn	0780388747	en_US
dc.identifier.isbn	9780780388741	en_US
dc.identifier.issn	1520-6149	en_US
dc.identifier.uri	http://hdl.handle.net/10453/16421
dc.description.abstract	In this paper, we develop a new linear matrix inequality (LMI) technique, which is practical for solutions of the general trigonometric seini-infinito linear constraint (TSIC) of competitive orders. Based on the new full LMI characterization for the convex hull of a trigonometric curve, it is shown that the semi-infini to optimization problem involving TSIC can be solved by LMI optimization problem with additional variables of dimension just n, the order of the the trigonometric curve. Our solution method is very robust which allows us to address almost all practical filter design problems. Unlike most previous works involving several complex mathematical tools, our derivation arguments are based on simple results of the convex analysis and some formal elementary transforms. Furthermore, many filter/filterbank design problems can be reformulated as the optimization of linear/convex quadratic objectives over the trigonometric semi-infinite constraints (TSIC). Based on this reformulation, these problems can be equivalently reduced to LMI optimization problems with the minimal size. Our examples of designing up to 1200-tap filters verifies the viability of our formulation. © 2005 IEEE.	en_US
dc.relation.ispartof	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings	en_US
dc.relation.isbasedon	10.1109/ICASSP.2005.1416036	en_US
dc.title	LMI characterization for the convex hull of trigonometric curves and applications	en_US
dc.type	Conference Proceeding
utslib.citation.volume	IV	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
dc.location.activity	Philadelphia, PA	en_US
dc.location.activity	WOS:000260823600003
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US
pubs.volume	IV	en_US

Abstract:

In this paper, we develop a new linear matrix inequality (LMI) technique, which is practical for solutions of the general trigonometric seini-infinito linear constraint (TSIC) of competitive orders. Based on the new full LMI characterization for the convex hull of a trigonometric curve, it is shown that the semi-infini to optimization problem involving TSIC can be solved by LMI optimization problem with additional variables of dimension just n, the order of the the trigonometric curve. Our solution method is very robust which allows us to address almost all practical filter design problems. Unlike most previous works involving several complex mathematical tools, our derivation arguments are based on simple results of the convex analysis and some formal elementary transforms. Furthermore, many filter/filterbank design problems can be reformulated as the optimization of linear/convex quadratic objectives over the trigonometric semi-infinite constraints (TSIC). Based on this reformulation, these problems can be equivalently reduced to LMI optimization problems with the minimal size. Our examples of designing up to 1200-tap filters verifies the viability of our formulation. © 2005 IEEE.

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http://hdl.handle.net/10453/16421