Generalized Chebyshev Function of Arbitrary Order With Real-Frequency Zero Pairs in an Explicit Rational Polynomial Expression

Jen Tsai Kuo; Chun Chin Wang; Chun Hung Lin; Philip A. Williams

doi:10.1109/APMC57107.2023.10439929

Generalized Chebyshev Function of Arbitrary Order With Real-Frequency Zero Pairs in an Explicit Rational Polynomial Expression

Jen Tsai Kuo^*, Chun Chin Wang, Chun Hung Lin, Philip A. Williams

^*Corresponding author for this work

Department of Electronic Engineering

Simutech Solution Corporation

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Generalized Chebyshev functions of an arbitrary order with up to three real-frequency zero pairs are derived in an explicit rational polynomial expression. Given in-band ripple level and positions of the zero pairs, numerator of the rational function is a sum of Chebyshev polynomials of the first kind weighted by constants specified by the zeros, and the denominator is simply a successive product of (a_i²-ω²), given that ± a_i are the designated real-frequency zero pair. Based on these analytical generalized Chebyshev filtering expressions, effort required by computer in synthesis of a lowpass prototype filter is at most a root-searching routine for polynomials. The whole synthesis process is straight-forward and needs neither iteration nor optimization.

Original language	English
Title of host publication	2023 Asia-Pacific Microwave Conference, APMC 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	147-149
Number of pages	3
ISBN (Electronic)	9781665494182
DOIs	https://doi.org/10.1109/APMC57107.2023.10439929
State	Published - 2023
Event	31st Asia-Pacific Microwave Conference, APMC 2023 - Taipei, Taiwan Duration: 05 12 2023 → 08 12 2023

Publication series

Name	Asia-Pacific Microwave Conference Proceedings, APMC
ISSN (Electronic)	2690-3946

Conference

Conference	31st Asia-Pacific Microwave Conference, APMC 2023
Country/Territory	Taiwan
City	Taipei
Period	05/12/23 → 08/12/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Keywords

cross coupling
filter synthesis
generalized Chebyshev function
low-pass prototype
transmission zero

Access to Document

10.1109/APMC57107.2023.10439929

Cite this

Kuo, J. T., Wang, C. C., Lin, C. H., & Williams, P. A. (2023). Generalized Chebyshev Function of Arbitrary Order With Real-Frequency Zero Pairs in an Explicit Rational Polynomial Expression. In 2023 Asia-Pacific Microwave Conference, APMC 2023 (pp. 147-149). (Asia-Pacific Microwave Conference Proceedings, APMC). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/APMC57107.2023.10439929

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abstract = "Generalized Chebyshev functions of an arbitrary order with up to three real-frequency zero pairs are derived in an explicit rational polynomial expression. Given in-band ripple level and positions of the zero pairs, numerator of the rational function is a sum of Chebyshev polynomials of the first kind weighted by constants specified by the zeros, and the denominator is simply a successive product of (ai2-ω2), given that ± ai are the designated real-frequency zero pair. Based on these analytical generalized Chebyshev filtering expressions, effort required by computer in synthesis of a lowpass prototype filter is at most a root-searching routine for polynomials. The whole synthesis process is straight-forward and needs neither iteration nor optimization.",

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Kuo, JT, Wang, CC, Lin, CH & Williams, PA 2023, Generalized Chebyshev Function of Arbitrary Order With Real-Frequency Zero Pairs in an Explicit Rational Polynomial Expression. in 2023 Asia-Pacific Microwave Conference, APMC 2023. Asia-Pacific Microwave Conference Proceedings, APMC, Institute of Electrical and Electronics Engineers Inc., pp. 147-149, 31st Asia-Pacific Microwave Conference, APMC 2023, Taipei, Taiwan, 05/12/23. https://doi.org/10.1109/APMC57107.2023.10439929

Generalized Chebyshev Function of Arbitrary Order With Real-Frequency Zero Pairs in an Explicit Rational Polynomial Expression. / Kuo, Jen Tsai; Wang, Chun Chin; Lin, Chun Hung et al.
2023 Asia-Pacific Microwave Conference, APMC 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 147-149 (Asia-Pacific Microwave Conference Proceedings, APMC).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - Generalized Chebyshev functions of an arbitrary order with up to three real-frequency zero pairs are derived in an explicit rational polynomial expression. Given in-band ripple level and positions of the zero pairs, numerator of the rational function is a sum of Chebyshev polynomials of the first kind weighted by constants specified by the zeros, and the denominator is simply a successive product of (ai2-ω2), given that ± ai are the designated real-frequency zero pair. Based on these analytical generalized Chebyshev filtering expressions, effort required by computer in synthesis of a lowpass prototype filter is at most a root-searching routine for polynomials. The whole synthesis process is straight-forward and needs neither iteration nor optimization.

AB - Generalized Chebyshev functions of an arbitrary order with up to three real-frequency zero pairs are derived in an explicit rational polynomial expression. Given in-band ripple level and positions of the zero pairs, numerator of the rational function is a sum of Chebyshev polynomials of the first kind weighted by constants specified by the zeros, and the denominator is simply a successive product of (ai2-ω2), given that ± ai are the designated real-frequency zero pair. Based on these analytical generalized Chebyshev filtering expressions, effort required by computer in synthesis of a lowpass prototype filter is at most a root-searching routine for polynomials. The whole synthesis process is straight-forward and needs neither iteration nor optimization.

KW - cross coupling

KW - filter synthesis

KW - generalized Chebyshev function

KW - low-pass prototype

KW - transmission zero

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Kuo JT, Wang CC, Lin CH, Williams PA. Generalized Chebyshev Function of Arbitrary Order With Real-Frequency Zero Pairs in an Explicit Rational Polynomial Expression. In 2023 Asia-Pacific Microwave Conference, APMC 2023. Institute of Electrical and Electronics Engineers Inc. 2023. p. 147-149. (Asia-Pacific Microwave Conference Proceedings, APMC). doi: 10.1109/APMC57107.2023.10439929

Generalized Chebyshev Function of Arbitrary Order With Real-Frequency Zero Pairs in an Explicit Rational Polynomial Expression

Abstract

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