A new constraint model for optimal design of constrained FIR digital filters

Magnitude-error and phase-error constrained optimal designs of finite impulse response (FIR) filters are nonconvex problems due to the nonconvexity of the lower-bound constraint of magnitude at any passband frequency point. In order to solve these problems, the nonconvex constraint region at an arbitrary passband frequency is usually approximated by a convex one. In this paper, a new convex constraint model is proposed. It approximates the nonconvex lower-bound magnitude constraint by a linear one while keeping the upper-bound magnitude and phase-error constraints unchanged. Design results demonstrate the effectiveness of the proposed constraint model and good performance of the designed filters.