A closed form solution to L2-sensitivity minimization of second-order state-space digital filters

Shunsuke Yamaki; Masahide Abe; Masayuki Kawamata

doi:10.1093/ietfec/e91-a.5.1268

A closed form solution to L₂-sensitivity minimization of second-order state-space digital filters

Shunsuke Yamaki, Masahide Abe, Masayuki Kawamata

Research output: Contribution to journal › Article

13 Citations (Scopus)

Abstract

This paper proposes a closed form solution to L₂-sensitivitym inimizationo f second-orders tate-spaced digital filters. Restricting ourselves to the second-order case of state-space digital filters, we can expresst he L₂-sensitivity by a simple linear combination of exponential functions and formulate the L₂-sensitivit my inimization problem by a simple polynomiale quation. As a result, the L₂-sensitivit my inimization problem can be converted into a problem to find the solution to a fourth-degree polynomiale quation of constantc oefficients which can be algebraically solved in closed form without iterative calculations.

Original language	English
Pages (from-to)	1268-1273
Number of pages	6
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E91-A
Issue number	5
DOIs	https://doi.org/10.1093/ietfec/e91-a.5.1268
Publication status	Published - 2008

Keywords

Closed form solution
State-space digital filters

ASJC Scopus subject areas

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

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10.1093/ietfec/e91-a.5.1268

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N2 - This paper proposes a closed form solution to L2-sensitivitym inimizationo f second-orders tate-spaced digital filters. Restricting ourselves to the second-order case of state-space digital filters, we can expresst he L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivit my inimization problem by a simple polynomiale quation. As a result, the L2-sensitivit my inimization problem can be converted into a problem to find the solution to a fourth-degree polynomiale quation of constantc oefficients which can be algebraically solved in closed form without iterative calculations.

AB - This paper proposes a closed form solution to L2-sensitivitym inimizationo f second-orders tate-spaced digital filters. Restricting ourselves to the second-order case of state-space digital filters, we can expresst he L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivit my inimization problem by a simple polynomiale quation. As a result, the L2-sensitivit my inimization problem can be converted into a problem to find the solution to a fourth-degree polynomiale quation of constantc oefficients which can be algebraically solved in closed form without iterative calculations.

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KW - State-space digital filters

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