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An L 1 ‐Approximation for the Design of FIR Digital Filters with Complex Coefficients
Author(s) -
MURAKAMI IKUYA,
MORI YUKIO,
AIKAWA NAOYUKI
Publication year - 2015
Publication title -
electronics and communications in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.131
H-Index - 13
eISSN - 1942-9541
pISSN - 1942-9533
DOI - 10.1002/ecj.11747
Subject(s) - passband , digital filter , approximation theory , overshoot (microwave communication) , approximation algorithm , mathematics , discontinuity (linguistics) , minimax approximation algorithm , finite impulse response , filter (signal processing) , filter design , algorithm , control theory (sociology) , computer science , band pass filter , mathematical analysis , electronic engineering , telecommunications , engineering , control (management) , artificial intelligence , computer vision
SUMMARY 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 flatter passband and a small overshoot around the discontinuity point as compared with the L 2 ‐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.