Gramian-preserving frequency transformation for state-space digital filters

Shunsuke Koshita; Masahide Abe; Masayuki Kawamata

doi:10.1109/APCCAS.2006.342382

Gramian-preserving frequency transformation for state-space digital filters

Shunsuke Koshita, Masahide Abe, Masayuki Kawamata

ENG - Electronic Engineering

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

2 Citations (Scopus)

Abstract

This paper proposes a new expression of frequency transformation for state-space digital filters. The proposed frequency transformation has the property of preserving the controllability Gramian and the observability Gramian of prototype state-space digital filters. This property shows that the proposed frequency transformation preserves the useful realizations of prototype digital filters such as minimum roundoff noise realizations, balanced realizations and limit cycle free realizations. Moreover, it is proved that the proposed frequency transformation retains an important inequality property with respect to the norm of the state transition matrix of limit cycle free digital filters. These results are derived from a modified formulation of Mullis and Roberts' frequency transformation and balanced realizations of allpass filters.

Original language	English
Title of host publication	APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems
Pages	1220-1223
Number of pages	4
DOIs	https://doi.org/10.1109/APCCAS.2006.342382
Publication status	Published - 2006
Event	APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems - , Singapore Duration: 2006 Dec 4 → 2006 Dec 6

Publication series

Name	IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS

Other

Other	APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems
Country/Territory	Singapore
Period	06/12/4 → 06/12/6

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/APCCAS.2006.342382

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Gramian-preserving frequency transformation for state-space digital filters. / Koshita, Shunsuke; Abe, Masahide; Kawamata, Masayuki.

APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems. 2006. p. 1220-1223 4145619 (IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS).

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

Koshita, S, Abe, M & Kawamata, M 2006, Gramian-preserving frequency transformation for state-space digital filters. in APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems., 4145619, IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS, pp. 1220-1223, APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems, Singapore, 06/12/4. https://doi.org/10.1109/APCCAS.2006.342382

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title = "Gramian-preserving frequency transformation for state-space digital filters",

abstract = "This paper proposes a new expression of frequency transformation for state-space digital filters. The proposed frequency transformation has the property of preserving the controllability Gramian and the observability Gramian of prototype state-space digital filters. This property shows that the proposed frequency transformation preserves the useful realizations of prototype digital filters such as minimum roundoff noise realizations, balanced realizations and limit cycle free realizations. Moreover, it is proved that the proposed frequency transformation retains an important inequality property with respect to the norm of the state transition matrix of limit cycle free digital filters. These results are derived from a modified formulation of Mullis and Roberts' frequency transformation and balanced realizations of allpass filters.",

author = "Shunsuke Koshita and Masahide Abe and Masayuki Kawamata",

year = "2006",

doi = "10.1109/APCCAS.2006.342382",

language = "English",

isbn = "1424403871",

series = "IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS",

pages = "1220--1223",

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note = "APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems ; Conference date: 04-12-2006 Through 06-12-2006",

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TY - GEN

T1 - Gramian-preserving frequency transformation for state-space digital filters

AU - Koshita, Shunsuke

AU - Abe, Masahide

AU - Kawamata, Masayuki

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Y1 - 2006

N2 - This paper proposes a new expression of frequency transformation for state-space digital filters. The proposed frequency transformation has the property of preserving the controllability Gramian and the observability Gramian of prototype state-space digital filters. This property shows that the proposed frequency transformation preserves the useful realizations of prototype digital filters such as minimum roundoff noise realizations, balanced realizations and limit cycle free realizations. Moreover, it is proved that the proposed frequency transformation retains an important inequality property with respect to the norm of the state transition matrix of limit cycle free digital filters. These results are derived from a modified formulation of Mullis and Roberts' frequency transformation and balanced realizations of allpass filters.

AB - This paper proposes a new expression of frequency transformation for state-space digital filters. The proposed frequency transformation has the property of preserving the controllability Gramian and the observability Gramian of prototype state-space digital filters. This property shows that the proposed frequency transformation preserves the useful realizations of prototype digital filters such as minimum roundoff noise realizations, balanced realizations and limit cycle free realizations. Moreover, it is proved that the proposed frequency transformation retains an important inequality property with respect to the norm of the state transition matrix of limit cycle free digital filters. These results are derived from a modified formulation of Mullis and Roberts' frequency transformation and balanced realizations of allpass filters.

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DO - 10.1109/APCCAS.2006.342382

M3 - Conference contribution

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SN - 9781424403875

T3 - IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS

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EP - 1223

BT - APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems

T2 - APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems

Y2 - 4 December 2006 through 6 December 2006

ER -

Gramian-preserving frequency transformation for state-space digital filters

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