No 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.

In this paper, we propose an L 1 -approximation for the design of FIR digital filters with complex coefficients. The L 1 -approximation has the advantage of having a flat passband and a small overshoot around the discontinuity point as compared with L 2 -approximation and L ∞ -approximation. As the obtained filter has complex coefficients, it can be reduced group delay and designed a digital filter with an asymmetric amplitude characteristic with respect to the origin. Algorithm proposed in this paper is based on Newton's method which is an efficient iterative approximation algorithm. We show effectiveness of the proposed method through a design example.

In this paper, we propose a design method of Hilbert Transformers using an L 1 error criterion. Conventional Hilbert transformers have been designed by using an L 2 error criterion or an L ∞ error criterion. In contrast, we use an L 1 error criterion for designing Hilbert Transformers. Therefore, compared with conventional design methods, the passband ripple is reduced. 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 that the vector space of the coefficients of the L 1 norm is a closed set and a convex set in order to ensure that the obtained solution is global optimal solution. Finally, we show the effectiveness of the proposed method through some examples.