A Closed Form Solution to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters
Summary :
This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of state-space digital filters, 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, the L2-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.5 pp.1268-1273
- Publication Date
- 2008/05/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e91-a.5.1268
- Type of Manuscript
- LETTER
- Category
- Digital Signal Processing
Authors
Keyword
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Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, "A Closed Form Solution to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 5, pp. 1268-1273, May 2008, doi: 10.1093/ietfec/e91-a.5.1268.
Abstract: This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of state-space digital filters, 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, the L2-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.5.1268/_p
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@ARTICLE{e91-a_5_1268,
author={Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Closed Form Solution to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters},
year={2008},
volume={E91-A},
number={5},
pages={1268-1273},
abstract={This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of state-space digital filters, 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, the L2-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.},
keywords={},
doi={10.1093/ietfec/e91-a.5.1268},
ISSN={1745-1337},
month={May},}
Copy
TY - JOUR
TI - A Closed Form Solution to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1268
EP - 1273
AU - Shunsuke YAMAKI
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2008
DO - 10.1093/ietfec/e91-a.5.1268
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2008
AB - This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of state-space digital filters, 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, the L2-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.
ER -
English
