A closed form solution to L2-sensitivity minimization of second-order digital filters subject to L2-scaling constraints

Shunsuke Yamaki; Masahide Abe; Masayuki Kawamata

doi:10.1109/APCCAS.2006.342361

A closed form solution to L2-sensitivity minimization of second-order digital filters subject to L2-scaling constraints

Shunsuke Yamaki, Masahide Abe, Masayuki Kawamata

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

1 Citation (Scopus)

Abstract

L₂-sensitivity is one of the functions that evaluates the coefficient quantization effects of state-space digital filters. This paper proposes a closed form solution to L₂-sensitivity minimization of 2nd-order state-space digital filters subject to L₂-scaling constraints. The proposed solution reduces a constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. Futhermore, by restricting ourselves to the case of 2nd-order state-space digital filters, we can formulate the L₂-sensitivity minimization problem via hyperbolic functions. As a result, we can express the L ₂-sensitivity in closed form, whose minimization subject to L ₂-scaling constraints is achieved without iterative calculations.

Original language	English
Title of host publication	APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems
Pages	1216-1219
Number of pages	4
DOIs	https://doi.org/10.1109/APCCAS.2006.342361
Publication status	Published - 2006 Dec 1
Event	APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems - , Singapore Duration: 2006 Dec 4 → 2006 Dec 6

Other

Other	APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems
Country	Singapore
Period	06/12/4 → 06/12/6

ASJC Scopus subject areas

Engineering(all)

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Yamaki, S , Abe, M & Kawamata, M 2006, A closed form solution to L2-sensitivity minimization of second-order digital filters subject to L2-scaling constraints. in APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems., 4145618, pp. 1216-1219, APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems, Singapore, 06/12/4. https://doi.org/10.1109/APCCAS.2006.342361

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abstract = "L2-sensitivity is one of the functions that evaluates the coefficient quantization effects of state-space digital filters. This paper proposes a closed form solution to L2-sensitivity minimization of 2nd-order state-space digital filters subject to L2-scaling constraints. The proposed solution reduces a constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. Futhermore, by restricting ourselves to the case of 2nd-order state-space digital filters, we can formulate the L2-sensitivity minimization problem via hyperbolic functions. As a result, we can express the L 2-sensitivity in closed form, whose minimization subject to L 2-scaling constraints is achieved without iterative calculations.",

author = "Shunsuke Yamaki and Masahide Abe and Masayuki Kawamata",

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doi = "10.1109/APCCAS.2006.342361",

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AU - Yamaki, Shunsuke

AU - Abe, Masahide

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PY - 2006/12/1

Y1 - 2006/12/1

N2 - L2-sensitivity is one of the functions that evaluates the coefficient quantization effects of state-space digital filters. This paper proposes a closed form solution to L2-sensitivity minimization of 2nd-order state-space digital filters subject to L2-scaling constraints. The proposed solution reduces a constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. Futhermore, by restricting ourselves to the case of 2nd-order state-space digital filters, we can formulate the L2-sensitivity minimization problem via hyperbolic functions. As a result, we can express the L 2-sensitivity in closed form, whose minimization subject to L 2-scaling constraints is achieved without iterative calculations.

AB - L2-sensitivity is one of the functions that evaluates the coefficient quantization effects of state-space digital filters. This paper proposes a closed form solution to L2-sensitivity minimization of 2nd-order state-space digital filters subject to L2-scaling constraints. The proposed solution reduces a constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. Futhermore, by restricting ourselves to the case of 2nd-order state-space digital filters, we can formulate the L2-sensitivity minimization problem via hyperbolic functions. As a result, we can express the L 2-sensitivity in closed form, whose minimization subject to L 2-scaling constraints is achieved without iterative calculations.

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ER -

A closed form solution to L2-sensitivity minimization of second-order digital filters subject to L2-scaling constraints

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