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

• Published in: 2006 IEEE Asia Pacific conference on circuits and systems : Singapore, 4-7 December 2006 pp. 1216 - 1219
• Main Authors: Yamaki, S., Abe, M., Kawamata, M.
• Format: Conference Proceeding
• Language: English; Japanese
• Published: IEEE 01.12.2006
• Subjects: Closed-form solution; Constraint optimization; Controllability; Covariance matrix; Digital filters; Equations; Observability; Quantization; Roundoff errors; Transfer functions
• ISBN: 9781424403868; 9781424403875; 1424403871; 1424403863
• DOI: 10.1109/APCCAS.2006.342361

L 2 -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 L 2 -sensitivity minimization of 2nd-order state-space digital filters subject to L 2 -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 L 2 -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