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This paper proposes synthesis of the minimum L2-sensitivity realizations of second-order digital filters without iterative calculations. We restrict ourselves to second-order digital filters and consider three cases of second-order digital filters: complex conjugate poles, distinct real poles, and multiple real poles. We can express the L2-sensitivity by a simple linear combination of exponential...
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 variable band-pass/band-stop infinite impulse response (IIR) state-space digital filters with high tuning accuracy and reduced computational complexity. We derive our proposed variable filters from the Gramian-preserving frequency transformation based on the normalized lattice structure of second-order all-pass functions. This approach gives a simple algorithm for control of the...
This paper proposes explicit expressions of the balanced realizations of second-order digital and analog filters. We first consider the case of digital filters. Second-order digital filters are categorized into the following three cases: complex conjugate poles, distinct real poles, and multiple real poles. For each case, simple formulas are derived for the synthesis of the balanced realizations....
This paper presents a new algorithm for realization of Gramian-preserving frequency transformation for linear discrete-time systems. In the proposed algorithm, we construct allpass systems for frequency transformation as the cascaded normalized lattice structure. It is shown that the frequency transformation based on this algorithm not only leaves the controllability/observability Gramians invariant...
This brief proposes a systematic approach to synthesis of limit cycle free state-space digital filters with minimum L2-sensitivity. We synthesize the minimum L2-sensitivity realization adopting the balanced realization as an initial realization. The coordinate transformation matrix which transforms the balanced realization into the minimum L2-sensitivity realization is expressed as the product of...
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