On L2-sensitivity of state-space digital filters under Gramian-preserving frequncy transformation

Shunsuke Koshita; Masahide Abe; Masayuki Kawamata

doi:10.1109/APSIPA.2013.6694188

On L₂-sensitivity of state-space digital filters under Gramian-preserving frequncy transformation

Shunsuke Koshita, Masahide Abe, Masayuki Kawamata

ENG - Electronic Engineering

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

Abstract

This paper aims to reveal the relationship between the minimum L ₂-sensitivity of state-space digital filters and the Gramian-preserving frequency transformation. To this end, we first give a prototype low-pass state-space filter in such a manner that its structure becomes the minimum L₂-sensitivity structure. Then we apply the Gramian-preserving (LP-LP) frequency transformation with a tunable parameter to this prototype filter. In this way we obtain a low-pass state-space filter with tunable cutoff frequency from a prescribed prototype low-pass filter with minimum L₂-sensitivity. For this tunable low-pass state-space filter, we evaluate the L₂-sensitivity over the entire range of cutoff frequencies. The evaluation result shows that, although the minimality of the L₂-sensitivity is not preserved under the frequency transformation, the L₂-sensitivity of the tunable filter given in this way becomes very close to the minimum value for arbitrary cutoff frequencies.

Original language	English
Title of host publication	2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013
DOIs	https://doi.org/10.1109/APSIPA.2013.6694188
Publication status	Published - 2013
Event	2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013 - Kaohsiung, Taiwan, Province of China Duration: 2013 Oct 29 → 2013 Nov 1

Publication series

Name	2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013

Other

Other	2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013
Country	Taiwan, Province of China
City	Kaohsiung
Period	13/10/29 → 13/11/1

ASJC Scopus subject areas

Information Systems
Signal Processing

Access to Document

10.1109/APSIPA.2013.6694188

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Koshita, S., Abe, M., & Kawamata, M. (2013). On L₂-sensitivity of state-space digital filters under Gramian-preserving frequncy transformation. In 2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013 [6694188] (2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013). https://doi.org/10.1109/APSIPA.2013.6694188

On L₂-sensitivity of state-space digital filters under Gramian-preserving frequncy transformation. / Koshita, Shunsuke; Abe, Masahide; Kawamata, Masayuki.

2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013. 2013. 6694188 (2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013).

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

Koshita, S, Abe, M & Kawamata, M 2013, On L₂-sensitivity of state-space digital filters under Gramian-preserving frequncy transformation. in 2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013., 6694188, 2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013, 2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013, Kaohsiung, Taiwan, Province of China, 13/10/29. https://doi.org/10.1109/APSIPA.2013.6694188

Koshita S, Abe M, Kawamata M. On L₂-sensitivity of state-space digital filters under Gramian-preserving frequncy transformation. In 2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013. 2013. 6694188. (2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013). https://doi.org/10.1109/APSIPA.2013.6694188

Koshita, Shunsuke ; Abe, Masahide ; Kawamata, Masayuki. / On L₂-sensitivity of state-space digital filters under Gramian-preserving frequncy transformation. 2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013. 2013. (2013 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2013).

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abstract = "This paper aims to reveal the relationship between the minimum L 2-sensitivity of state-space digital filters and the Gramian-preserving frequency transformation. To this end, we first give a prototype low-pass state-space filter in such a manner that its structure becomes the minimum L2-sensitivity structure. Then we apply the Gramian-preserving (LP-LP) frequency transformation with a tunable parameter to this prototype filter. In this way we obtain a low-pass state-space filter with tunable cutoff frequency from a prescribed prototype low-pass filter with minimum L2-sensitivity. For this tunable low-pass state-space filter, we evaluate the L2-sensitivity over the entire range of cutoff frequencies. The evaluation result shows that, although the minimality of the L2-sensitivity is not preserved under the frequency transformation, the L2-sensitivity of the tunable filter given in this way becomes very close to the minimum value for arbitrary cutoff frequencies.",

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

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N2 - This paper aims to reveal the relationship between the minimum L 2-sensitivity of state-space digital filters and the Gramian-preserving frequency transformation. To this end, we first give a prototype low-pass state-space filter in such a manner that its structure becomes the minimum L2-sensitivity structure. Then we apply the Gramian-preserving (LP-LP) frequency transformation with a tunable parameter to this prototype filter. In this way we obtain a low-pass state-space filter with tunable cutoff frequency from a prescribed prototype low-pass filter with minimum L2-sensitivity. For this tunable low-pass state-space filter, we evaluate the L2-sensitivity over the entire range of cutoff frequencies. The evaluation result shows that, although the minimality of the L2-sensitivity is not preserved under the frequency transformation, the L2-sensitivity of the tunable filter given in this way becomes very close to the minimum value for arbitrary cutoff frequencies.

AB - This paper aims to reveal the relationship between the minimum L 2-sensitivity of state-space digital filters and the Gramian-preserving frequency transformation. To this end, we first give a prototype low-pass state-space filter in such a manner that its structure becomes the minimum L2-sensitivity structure. Then we apply the Gramian-preserving (LP-LP) frequency transformation with a tunable parameter to this prototype filter. In this way we obtain a low-pass state-space filter with tunable cutoff frequency from a prescribed prototype low-pass filter with minimum L2-sensitivity. For this tunable low-pass state-space filter, we evaluate the L2-sensitivity over the entire range of cutoff frequencies. The evaluation result shows that, although the minimality of the L2-sensitivity is not preserved under the frequency transformation, the L2-sensitivity of the tunable filter given in this way becomes very close to the minimum value for arbitrary cutoff frequencies.

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