Some Algorithms for the Recursive Input-Output Modeling of 2-D Systems

Résumé du livre

This paper considers the deterministic and stochastic modeling of 2-D systems described by their input/output data. In the deterministic case, the modeling problem is formulated as a 2-D Pade approximation problem. By studying several possible geometries of approximation, we obtain several sets of recursions of the 2-D rational approximants. These results exploit the properties of 2-D Hankel matrices, and they are used here to characterize the 2-D rational transfer functions. In the stochastic case, the realization problem is viewed as a 2-D prediction problem. This problem is solved recursively by generalizing to the 2-D case an algorithm due to Levinson in the 1-D case. The predictors obtained by this algorithm are then showed to converge to the 2-D spectral factors of the output spectrum. (Author).