An L₁‐Approximation for the Design of FIR Digital Filters with Complex Coefficients

Abstract

SUMMARY In this paper, we propose an L1‐approximation for the design of FIR digital filters with complex coefficients. The L1‐approximation has the advantage of having a flatter passband and a small overshoot around the discontinuity point as compared with the L2‐approximation and L∞‐approximation. As the obtained filter has complex coefficients, it is possible to reduce group delay and to design a digital filter with a asymmetric amplitude characteristic with respect to the origin. The algorithm proposed in this paper is based on Newton's method, which is an efficient iterative approximation algorithm. We show the effectiveness of the proposed method through a design example.