Matrix analysis
Digital signal processing
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Parametrizations in Control, Estimation, and Filtering Problems: Accuracy Aspects
Parametrizations in Control, Estimation, and Filtering Problems: Accuracy Aspects
Fast communication: An improved orthogonal digital filter structure
Signal Processing
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It is well known that normal realizations are free of limit cycles and that a digital filter implemented with a state-space realization (A,B,C,d) has no limit cycles if there exists some diagonal matrix D0 such that D-A^TDA=0. In this brief, a method is proposed to check the existence of such a D for any given realization. It is also shown that the normal realizations have a minimal error propagation gain. More interestingly, the normal realizations are characterized, the minimum roundoff noise normal realization problem is formulated and solved analytically. An example is presented to test the efficiency of the proposed method and to demonstrate the performance of the proposed optimal normal realizations.