Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for Second-Order State-Space Digital Filters with Real Poles
Summary :
This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.2 pp.476-487
- Publication Date
- 2010/02/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E93.A.476
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
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Keyword
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Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, "Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for Second-Order State-Space Digital Filters with Real Poles" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 2, pp. 476-487, February 2010, doi: 10.1587/transfun.E93.A.476.
Abstract: This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.476/_p
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@ARTICLE{e93-a_2_476,
author={Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for Second-Order State-Space Digital Filters with Real Poles},
year={2010},
volume={E93-A},
number={2},
pages={476-487},
abstract={This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.},
keywords={},
doi={10.1587/transfun.E93.A.476},
ISSN={1745-1337},
month={February},}
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TY - JOUR
TI - Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for Second-Order State-Space Digital Filters with Real Poles
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 476
EP - 487
AU - Shunsuke YAMAKI
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2010
DO - 10.1587/transfun.E93.A.476
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2010
AB - This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.
ER -
English
