Closed form expressions of the minimum L2-sensitivity realizations for all-pass digital filters

Shunsuke Yamaki; Masahide Abe; Masayuki Kawamata

doi:10.1109/ICNIDC.2010.5657944

Closed form expressions of the minimum L₂-sensitivity realizations for all-pass digital filters

Shunsuke Yamaki, Masahide Abe, Masayuki Kawamata

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

Abstract

This paper presents closed form expressions of the minimum L ₂-sensitivity realizations of all-pass digital filters. We first prove that the L₂-sensitivity minimization problem can be solved analytically if the all second-order modes of a digital filter are equal. We focus on the fact that the second-order modes of all-pass digital filters are all unity. As a result, it is clarified that the minimum L₂- sensitivity realization of an all-pass digital filter is equal to the balanced realization, of which closed form expression can be derived analytically.

Original language	English
Title of host publication	Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010
Pages	977-981
Number of pages	5
DOIs	https://doi.org/10.1109/ICNIDC.2010.5657944
Publication status	Published - 2010 Dec 1
Event	2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010 - Beijing, China Duration: 2010 Sept 24 → 2010 Sept 26

Publication series

Name	Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010

Other

Other	2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010
Country/Territory	China
City	Beijing
Period	10/9/24 → 10/9/26

Keywords

All-pass digital filters
Minimum L -sensitivity realizations
Second-order modes
State-space digital filters

ASJC Scopus subject areas

Computer Networks and Communications
Hardware and Architecture

Access to Document

10.1109/ICNIDC.2010.5657944

Cite this

Yamaki, S., Abe, M., & Kawamata, M. (2010). Closed form expressions of the minimum L₂-sensitivity realizations for all-pass digital filters. In Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010 (pp. 977-981). [5657944] (Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010). https://doi.org/10.1109/ICNIDC.2010.5657944

Closed form expressions of the minimum L₂-sensitivity realizations for all-pass digital filters. / Yamaki, Shunsuke; Abe, Masahide; Kawamata, Masayuki.
Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010. 2010. p. 977-981 5657944 (Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010).

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

Yamaki, S, Abe, M & Kawamata, M 2010, Closed form expressions of the minimum L₂-sensitivity realizations for all-pass digital filters. in Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010., 5657944, Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010, pp. 977-981, 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010, Beijing, China, 10/9/24. https://doi.org/10.1109/ICNIDC.2010.5657944

Yamaki S, Abe M, Kawamata M. Closed form expressions of the minimum L₂-sensitivity realizations for all-pass digital filters. In Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010. 2010. p. 977-981. 5657944. (Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010). doi: 10.1109/ICNIDC.2010.5657944

Yamaki, Shunsuke ; Abe, Masahide ; Kawamata, Masayuki. / Closed form expressions of the minimum L₂-sensitivity realizations for all-pass digital filters. Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010. 2010. pp. 977-981 (Proceedings - 2010 2nd IEEE International Conference on Network Infrastructure and Digital Content, IC-NIDC 2010).

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abstract = "This paper presents closed form expressions of the minimum L 2-sensitivity realizations of all-pass digital filters. We first prove that the L2-sensitivity minimization problem can be solved analytically if the all second-order modes of a digital filter are equal. We focus on the fact that the second-order modes of all-pass digital filters are all unity. As a result, it is clarified that the minimum L2- sensitivity realization of an all-pass digital filter is equal to the balanced realization, of which closed form expression can be derived analytically.",

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