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SUMMARY This paper proposes a closed form solution to L 2-sensitivity minimization of second-order state-space digital filters subject to L 2-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… (More)

— This paper proposes a novel approach to L2-sensitivity minimization problem of 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. As a result, iterative algorithms for the L2-sensitivity… (More)

—This letter presents explicit expressions of the balanced realization of second-order digital filters with real poles. We consider two cases of second-order digital filters: that of real and distinct poles and that of real and multiple poles. Simple formulas are derived for the synthesis of the balanced realizations of these second-order digital filters.

—This brief proposes a systematic approach to synthesis of limit cycle free state-space digital filters with minimum 2-sensitivity. We synthesize the minimum 2-sensitivity realization adopting the balanced realization as an initial realization. The coordinate transformation matrix which transforms the balanced realization into the minimum 2-sensitivity… (More)

— This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the 2-nd order case of state-space digital filters, we can formulate L2-sensitivity minimization problem by hyperbolic functions. As a result, L2-sensitivity minimization problem can be converted into a problem to… (More)

SUMMARY 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 second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an… (More)

— This paper proposes analytical synthesis of the minimum L2-sensitivity realizations of all-pass digital filters. We first prove that the L2-sensitivity minimization problem can be solved analytically if the all second-order modes of a digital filter are equal. We focus on the fact that the second-order modes of all-pass digital filters are all unity. As a… (More)

SUMMARY This letter proposes closed form solutions to the L 2-sensitivity minimization of second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. In case of second-order digital filters, we can express the L 2-sensitivity of second-order digital filters by… (More)