A Synthesis of Complex Allpass Circuits Using the Factorization of Scattering Matrices--Explicit Formulae for Even-Order Real Complementary Filters Having Butterworth or Chebyshev Responses--

Nobuo MURAKOSHI; Eiji WATANABE; Akinori NISHIHARA

A Synthesis of Complex Allpass Circuits Using the Factorization of Scattering Matrices--Explicit Formulae for Even-Order Real Complementary Filters Having Butterworth or Chebyshev Responses--

Nobuo MURAKOSHI, Eiji WATANABE, Akinori NISHIHARA

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Low-sensitivity digital filters are required for accurate signal processing. Among many low-sensitivity digital filters, a method using complex allpass circuits is well-known. In this paper, a new synthesis of complex allpass circuits is proposed. The proposed synthesis can be realized more easily either only in the z-domain or in the s-domain than conventional methods. The key concept for the synthesis is based on the factorization of lossless scattering matrices. Complex allpass circuits are interpreted as lossless digital two-port circuits, whose scattering matrices are factored. Furthermore, in the cases of Butterworth, Chebyshev and inverse Chebyshev responses, the explicit formulae for multiplier coefficients are derived, which enable us to synthesize the objective circuits directly from the specifications in the s-domain. Finally design examples verify the effectiveness of the proposed method.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.3 pp.317-325

Publication Date: 1993/03/25

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Type of Manuscript: Special Section PAPER (Special Section on the 5th Karuizawa Workshop on Circuits and Systems)

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Nobuo MURAKOSHI, Eiji WATANABE, Akinori NISHIHARA, "A Synthesis of Complex Allpass Circuits Using the Factorization of Scattering Matrices--Explicit Formulae for Even-Order Real Complementary Filters Having Butterworth or Chebyshev Responses--" in IEICE TRANSACTIONS on Fundamentals, vol. E76-A, no. 3, pp. 317-325, March 1993, doi: .
Abstract: Low-sensitivity digital filters are required for accurate signal processing. Among many low-sensitivity digital filters, a method using complex allpass circuits is well-known. In this paper, a new synthesis of complex allpass circuits is proposed. The proposed synthesis can be realized more easily either only in the z-domain or in the s-domain than conventional methods. The key concept for the synthesis is based on the factorization of lossless scattering matrices. Complex allpass circuits are interpreted as lossless digital two-port circuits, whose scattering matrices are factored. Furthermore, in the cases of Butterworth, Chebyshev and inverse Chebyshev responses, the explicit formulae for multiplier coefficients are derived, which enable us to synthesize the objective circuits directly from the specifications in the s-domain. Finally design examples verify the effectiveness of the proposed method.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e76-a_3_317/_p

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@ARTICLE{e76-a_3_317,
author={Nobuo MURAKOSHI, Eiji WATANABE, Akinori NISHIHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Synthesis of Complex Allpass Circuits Using the Factorization of Scattering Matrices--Explicit Formulae for Even-Order Real Complementary Filters Having Butterworth or Chebyshev Responses--},
year={1993},
volume={E76-A},
number={3},
pages={317-325},
abstract={Low-sensitivity digital filters are required for accurate signal processing. Among many low-sensitivity digital filters, a method using complex allpass circuits is well-known. In this paper, a new synthesis of complex allpass circuits is proposed. The proposed synthesis can be realized more easily either only in the z-domain or in the s-domain than conventional methods. The key concept for the synthesis is based on the factorization of lossless scattering matrices. Complex allpass circuits are interpreted as lossless digital two-port circuits, whose scattering matrices are factored. Furthermore, in the cases of Butterworth, Chebyshev and inverse Chebyshev responses, the explicit formulae for multiplier coefficients are derived, which enable us to synthesize the objective circuits directly from the specifications in the s-domain. Finally design examples verify the effectiveness of the proposed method.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - A Synthesis of Complex Allpass Circuits Using the Factorization of Scattering Matrices--Explicit Formulae for Even-Order Real Complementary Filters Having Butterworth or Chebyshev Responses--
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 317
EP - 325
AU - Nobuo MURAKOSHI
AU - Eiji WATANABE
AU - Akinori NISHIHARA
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1993
AB - Low-sensitivity digital filters are required for accurate signal processing. Among many low-sensitivity digital filters, a method using complex allpass circuits is well-known. In this paper, a new synthesis of complex allpass circuits is proposed. The proposed synthesis can be realized more easily either only in the z-domain or in the s-domain than conventional methods. The key concept for the synthesis is based on the factorization of lossless scattering matrices. Complex allpass circuits are interpreted as lossless digital two-port circuits, whose scattering matrices are factored. Furthermore, in the cases of Butterworth, Chebyshev and inverse Chebyshev responses, the explicit formulae for multiplier coefficients are derived, which enable us to synthesize the objective circuits directly from the specifications in the s-domain. Finally design examples verify the effectiveness of the proposed method.
ER -