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This paper presents a new realization method of variable low-pass infinite impulse response (IIR) digital filters with high tuning accuracy. We construct the proposed variable filters by using the state-space-based frequency transformation proposed by Mullis and Roberts. Since this transformation requires an inverse matrix that leads to high computational cost, we present a new simple algorithm that...
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 note discusses a relationship between the Hankel singular values and reflected zeros of linear systems. Our main result proves that the Hankel singular values of a linear continuous-time system increase (decrease) pointwise when one or more zeros of the transfer function are reflected with respect to the imaginary axis, that is, move from the left-(right-)half to the right-(left-)half of the...
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 paper presents a new analysis of power complementary analog filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. We show that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to...
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...
This paper proposes a new expression of frequency transformation for linear continuous-time state-space systems. The proposed frequency transformation preserves the controllability Gramian and the observability Gramian of prototype state-space systems, and thus allows us to easily realize various kinds of state-space systems keeping the same realization as that of prototype state-space systems. Our...
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