SUMMARYIn this paper, the design of constrained linear phase ÿnite impulse response (FIR) ÿlters is considered. The problem is formulated as a linear complementarity problem (LCP), which is solved using Lemke's algorithm. The LCP is a reÿned mathematical formalism with useful theoretical results. The digital ÿlters presented meet e ciently the speciÿcations of the magnitude response error. The used algorithm is a direct one and therefore, there is no need for matrix inversion. However, in the iterative methods that are frequently used, the bulk of the design computation is concerned with the evaluation of matrix inversion in order to solve a system of equations. Examples to illustrate the proposed method are presented.

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