Closed form solutions to l 2-sensitivity minimization subject to l 2-scaling constraints for second-order state-space digital filters with real poles

Shunsuke Yamaki, Masahide Abe, Masayuki Kawamata

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

This paper proposes closed form solutions to the L 2-sensitivity minimization subject to L 2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of secondorder 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 L 2-sensitivity by a simple linear combination of exponential functions and formulate the L 2-sensitivity minimization problem by a simple polynomial equation. As a result, L 2-sensitivity is expressed in closed form, and its minimization subject to L 2-scaling constraints is.

Original languageEnglish
Pages (from-to)476-487
Number of pages12
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE93-A
Issue number2
DOIs
Publication statusPublished - 2010 Feb

Keywords

  • Closed form solutions
  • Second-order digital filters with real poles
  • Variable transformation

ASJC Scopus subject areas

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

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