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A unified approach for the design of 2-D digital filters via semidefinite programming

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1 Author(s)
Lu, W.-S. ; Dept. of Electr. & Comput. Eng., Victoria Univ., BC, Canada

This paper attempts to demonstrate that a modem optimization methodology known as semidefinite programming (SDP) can serve as the algorithmic core of a unified design tool for a variety of two-dimensional (2-D) digital filters. Representative SDP-based designs presented in the paper include minimax and weighted least-squares designs of FIR filters with continuous and discrete coefficients, and minimax design of stable separable-denominator IIR filters. Our studies are motivated by the fact that SDP as a subclass of convex programming can be solved efficiently using recently developed interior-point methods and, more importantly, constraints on amplitude/phase responses in certain frequency regions and on stability (for IIR filters), that are often encountered in many filter design problems, can be formulated in a natural way as linear matrix inequalities (LMI) which allow SDP to apply. Design examples for each class of filters are included to demonstrate that SDP-based methods can in many cases be useful in producing optimal or near-optimal 2-D filters with reduced computational complexity

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:49 ,  Issue: 6 )