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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 discusses synthesis of state-space digital filters with minimum L 2-sensitivity. Restricting ourselves to the 2-nd order case of state-space digital filters, we can represent L 2-sensitivity in closed form. As a result, L 2-sensitivity minimization problem is converted into a problem to find the solution to a 4-th degree equation of constant… (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)

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)

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)

— 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)

—This paper reveals the class of digital filters with all second-order modes equal. We first prove that if the second-order modes of a digital filter are all equal, the-sensitivity minimization problem of the digital filter can be solved analytically. We derive a general expression of the transfer function of digital filters with all second-order modes… (More)