LMI characterization for the convex hull of trigonometric curves and applications

HD Tuan, TT Son, Ba-Ngu Vo, TQ Nguyen

    Research output: Chapter in Book/Conference paperConference paper

    3 Citations (Web of Science)

    Abstract

    In this paper, we develop a new linear matrix inequality (LW technique, which is practical for solutions of the general trigonometric semi-infinite 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-infinite 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.
    Original languageEnglish
    Title of host publication2005 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1-5
    Place of PublicationUSA
    PublisherIEEE, Institute of Electrical and Electronics Engineers
    Pages425-428
    Volume5
    ISBN (Print)0780388747
    Publication statusPublished - 2005
    Event2005 IEEE International Conference on Acoustics, Speech, and Signal Processing - Philadelphia, United States
    Duration: 18 Mar 200523 Mar 2005

    Conference

    Conference2005 IEEE International Conference on Acoustics, Speech, and Signal Processing
    Abbreviated titleICASSP 2005
    Country/TerritoryUnited States
    CityPhiladelphia
    Period18/03/0523/03/05

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