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

Shunsuke YAMAKI  Masahide ABE  Masayuki KAWAMATA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.7   pp.1697-1705
Publication Date: 2008/07/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.7.1697
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
state-space digital filters,  L2-sensitivity,  variable transformation,  closed form solution,  

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Summary: 
This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters subject to L2-scaling constraints. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. Furthermore, restricting ourselves to the case of second-order 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, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.