Synthesis of low‐sensitivity second‐order real digital filters using complex two‐port adapters

Nobuo Murakoshi, Akinori Nishihara, Eiji Watanabe

Research output: Contribution to journalArticle

Abstract

If complex coefficients are used in the realization of the real‐coefficient transfer function, the degree of freedom in the circuit construction is enhanced. This creates a possibility that a lower‐sensitivity filter can be realized than in the traditional low‐sensitivity filter using the real coefficients. This paper discusses a method to construct the second‐order real‐coefficient IIR filter using the complex two‐port adapter. First, by using the complex two‐port adapter, a method for circuit construction is proposed where the second‐order bandpass, lowpass, high‐pass, and asymmetrical bandstop transfer functions are realized. The proposed circuit can be realized with fewer number of multipliers than the conventional circuits using complex coefficients. Then a method is shown which selects the complex two‐port adapter according to the value of the real part of the coefficient of the complex multiplier. By this selection method, the circuit with the lowest sensitivity in regard to the real part can be realized without increasing the computational complexity for the circuit. Furthermore, a method is considered to reduce the sensitivity also for the imaginary part of the complex multiplier coefficient. Finally, using a simple example, it is verified that the circuit obtained by the proposed construction method has the low sensitivity.

Original languageEnglish
Pages (from-to)31-39
Number of pages9
JournalElectronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
Volume76
Issue number1
DOIs
Publication statusPublished - 1993

Fingerprint

Digital filters
Networks (circuits)
Transfer functions
IIR filters
Computational complexity

Keywords

  • Complex coefficient
  • digital filter
  • low sensitivity
  • two‐port adapter

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

@article{e7c451fd9239421996132ef936b84f0f,
title = "Synthesis of low‐sensitivity second‐order real digital filters using complex two‐port adapters",
abstract = "If complex coefficients are used in the realization of the real‐coefficient transfer function, the degree of freedom in the circuit construction is enhanced. This creates a possibility that a lower‐sensitivity filter can be realized than in the traditional low‐sensitivity filter using the real coefficients. This paper discusses a method to construct the second‐order real‐coefficient IIR filter using the complex two‐port adapter. First, by using the complex two‐port adapter, a method for circuit construction is proposed where the second‐order bandpass, lowpass, high‐pass, and asymmetrical bandstop transfer functions are realized. The proposed circuit can be realized with fewer number of multipliers than the conventional circuits using complex coefficients. Then a method is shown which selects the complex two‐port adapter according to the value of the real part of the coefficient of the complex multiplier. By this selection method, the circuit with the lowest sensitivity in regard to the real part can be realized without increasing the computational complexity for the circuit. Furthermore, a method is considered to reduce the sensitivity also for the imaginary part of the complex multiplier coefficient. Finally, using a simple example, it is verified that the circuit obtained by the proposed construction method has the low sensitivity.",
keywords = "Complex coefficient, digital filter, low sensitivity, two‐port adapter",
author = "Nobuo Murakoshi and Akinori Nishihara and Eiji Watanabe",
year = "1993",
doi = "10.1002/ecjc.4430760104",
language = "English",
volume = "76",
pages = "31--39",
journal = "Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)",
issn = "1042-0967",
publisher = "John Wiley and Sons Inc.",
number = "1",

}

TY - JOUR

T1 - Synthesis of low‐sensitivity second‐order real digital filters using complex two‐port adapters

AU - Murakoshi, Nobuo

AU - Nishihara, Akinori

AU - Watanabe, Eiji

PY - 1993

Y1 - 1993

N2 - If complex coefficients are used in the realization of the real‐coefficient transfer function, the degree of freedom in the circuit construction is enhanced. This creates a possibility that a lower‐sensitivity filter can be realized than in the traditional low‐sensitivity filter using the real coefficients. This paper discusses a method to construct the second‐order real‐coefficient IIR filter using the complex two‐port adapter. First, by using the complex two‐port adapter, a method for circuit construction is proposed where the second‐order bandpass, lowpass, high‐pass, and asymmetrical bandstop transfer functions are realized. The proposed circuit can be realized with fewer number of multipliers than the conventional circuits using complex coefficients. Then a method is shown which selects the complex two‐port adapter according to the value of the real part of the coefficient of the complex multiplier. By this selection method, the circuit with the lowest sensitivity in regard to the real part can be realized without increasing the computational complexity for the circuit. Furthermore, a method is considered to reduce the sensitivity also for the imaginary part of the complex multiplier coefficient. Finally, using a simple example, it is verified that the circuit obtained by the proposed construction method has the low sensitivity.

AB - If complex coefficients are used in the realization of the real‐coefficient transfer function, the degree of freedom in the circuit construction is enhanced. This creates a possibility that a lower‐sensitivity filter can be realized than in the traditional low‐sensitivity filter using the real coefficients. This paper discusses a method to construct the second‐order real‐coefficient IIR filter using the complex two‐port adapter. First, by using the complex two‐port adapter, a method for circuit construction is proposed where the second‐order bandpass, lowpass, high‐pass, and asymmetrical bandstop transfer functions are realized. The proposed circuit can be realized with fewer number of multipliers than the conventional circuits using complex coefficients. Then a method is shown which selects the complex two‐port adapter according to the value of the real part of the coefficient of the complex multiplier. By this selection method, the circuit with the lowest sensitivity in regard to the real part can be realized without increasing the computational complexity for the circuit. Furthermore, a method is considered to reduce the sensitivity also for the imaginary part of the complex multiplier coefficient. Finally, using a simple example, it is verified that the circuit obtained by the proposed construction method has the low sensitivity.

KW - Complex coefficient

KW - digital filter

KW - low sensitivity

KW - two‐port adapter

UR - http://www.scopus.com/inward/record.url?scp=84989432338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84989432338&partnerID=8YFLogxK

U2 - 10.1002/ecjc.4430760104

DO - 10.1002/ecjc.4430760104

M3 - Article

VL - 76

SP - 31

EP - 39

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 1042-0967

IS - 1

ER -