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

Research output: Contribution to journalArticle

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 formulate 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.

Original languageEnglish
Pages (from-to)317-325
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE76-A
Issue number3
Publication statusPublished - 1993 Mar
Externally publishedYes

Fingerprint

Chebyshev filters
Butterworth filters
Factorization
Scattering
Networks (circuits)
Digital filters
Signal processing
Specifications

ASJC Scopus subject areas

  • Hardware and Architecture
  • Information Systems
  • Electrical and Electronic Engineering

Cite this

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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 formulate 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.",
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