LMI characterization for the convex hull of trigonometric curves and applications

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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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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