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This paper presents closed form expressions 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...
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...
This paper proposes a new expression of frequency transformation for state-space digital filters. The proposed frequency transformation has the property of preserving the controllability Gramian and the observability Gramian of prototype state-space digital filters. This property shows that the proposed frequency transformation preserves the useful realizations of prototype digital filters such as...
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