State-Space Analysis of Power Complementary Filters
Summary :
This paper presents a new analysis of power complementary filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. Through this new state-space analysis of power complementary filters, we prove that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result shows that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems. Finally, we give a numerical example to demonstrate our results.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.10 pp.2265-2271
- Publication Date
- 2007/10/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e90-a.10.2265
- Type of Manuscript
- PAPER
- Category
- Analog Signal Processing
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Keyword
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Shunsuke KOSHITA, Masahide ABE, Masayuki KAWAMATA, "State-Space Analysis of Power Complementary Filters" in IEICE TRANSACTIONS on Fundamentals,
vol. E90-A, no. 10, pp. 2265-2271, October 2007, doi: 10.1093/ietfec/e90-a.10.2265.
Abstract: This paper presents a new analysis of power complementary filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. Through this new state-space analysis of power complementary filters, we prove that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result shows that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems. Finally, we give a numerical example to demonstrate our results.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.10.2265/_p
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@ARTICLE{e90-a_10_2265,
author={Shunsuke KOSHITA, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={State-Space Analysis of Power Complementary Filters},
year={2007},
volume={E90-A},
number={10},
pages={2265-2271},
abstract={This paper presents a new analysis of power complementary filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. Through this new state-space analysis of power complementary filters, we prove that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result shows that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems. Finally, we give a numerical example to demonstrate our results.},
keywords={},
doi={10.1093/ietfec/e90-a.10.2265},
ISSN={1745-1337},
month={October},}
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TY - JOUR
TI - State-Space Analysis of Power Complementary Filters
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2265
EP - 2271
AU - Shunsuke KOSHITA
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2007
DO - 10.1093/ietfec/e90-a.10.2265
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2007
AB - This paper presents a new analysis of power complementary filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. Through this new state-space analysis of power complementary filters, we prove that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result shows that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems. Finally, we give a numerical example to demonstrate our results.
ER -
English
