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 journalArticlepeer-review

13 Citations (Scopus)


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 languageEnglish
Pages (from-to)1268-1273
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number5
Publication statusPublished - 2008


  • 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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