Ikuya Murakami and Naoyuki Aikawa
FIR digital filter, Hilbert transformer, L1 norm, POCS
In this paper, we propose a design method of Hilbert Transformers using an L1 error criterion. Conventional Hilbert transformers have been designed by using an L2 error criterion or an L∞error criterion. In contrast, we use an L1 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 L1 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.
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