In this paper, we propose an L1-method for the design of finite impulse response (FIR) digital filters with complex coefficients. An L1-method has the advantage of having a flat passband and a small overshoot around the discontinuity point, as compared with the L2-method and the L∞-method. With complex coefficients, we can reduce group delay and can design a digital filter with an asymmetric amplitude characteristic with respect to the origin. The algorithm proposed in this paper is based on the projection onto convex sets (POCS) method, which is an efficient iterative approximation algorithm. We show the effectiveness of the proposed method through a design example.
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