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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 result, it is clarified that the minimum L...
L2-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 L2-sensitivity minimization of 2nd-order state-space digital filters subject to L2 -scaling constraints. The proposed solution reduces a constrained optimization problem to an unconstrained optimization problem by appropriate variable...
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 minimization without L2-scaling constraints can be applied...
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