IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2008 E91-A(5):1268-1273; doi:10.1093/ietfec/e91-a.5.1268

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Copyright © 2008 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Letters -- Digital Signal Processing

A Closed Form Solution to L₂-Sensitivity Minimization of Second-Order State-Space Digital Filters

Shunsuke YAMAKI¹, Masahide ABE¹ and Masayuki KAWAMATA¹

¹ The authors are with the Department of Electronic Engineering, Graduate School of Engineering, Tohoku University, Sendaishi, 980-8579 Japan. E-mail: yamaki{at}mk.ecei.tohoku.ac.jp, E-mail: masahide{at}mk.ecei.tohoku.ac.jp, E-mail: kawamata{at}mk.ecei.tohoku.ac.jp

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.

Key Words: state-space digital filters, L₂-sensitivity, minimization, closed form solution

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Manuscript received January 8, 2008.

References

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by YAMAKI, S. Articles by KAWAMATA, M. Social Bookmarking          What's this?