Sufficient conditions for the nonexistence of limit cycles in two-dimensional digital filters
N. El-Agizi, Moustafa M. Fahmy · IEEE Transactions on Circuits and Systems · 1979
The stability of the two classes of two-dimensional digital filters defined byF1: x_{i+1,j+1} = Q_R[ax_{i+1,j}+bx_{i,j+1}+cx_{i,j}]andF2: x_{i+1,j+1} = Q_R[ax_{i+1,j}]+Q_R[bx_{i,j+1}]is studied. HereQ_Ris the rounding operator, and fixed-point arithmetic is used. Sufficient conditions for the stability ofF1and necessary and sufficient conditions for the stability ofF2are derived. For the more general case of higher order two-dimensional (2-D) digital filters, sufficient conditions for the nonexistence of separable 2-D limit cycles are derived by extending the results of Claasen et al. [1].