New Results in 2-D Systems Theory. Part III. Recursive Realization and Estimation Algorithms for 2-D Systems.

摘要

In this paper realization procedures for 2-D systems are discussed from an input/output point of view (leaving the state-space approach for further studies). Stochastic as well as deterministic techniques of realization are presented. In the stochastic case the Levinson algorithm is generalized to the 2-D case. The 2-D Levinson recursions are related to similar recursions for 2-D orthogonal polynomials on the unit hyper circle generalizations of the Szego polynomials. These recursions are connected to the factorizations of the block covariance matrix in elements which are causal in each of the four quadrants. Furthermore, 2-D maximum-entropy spectral analysis techniques are discussed. From a deterministic standpoint several recursive partial realization schemes are considered, which represent fast solutions of the 2-D Pade approximation problem. These methods are extensions of the Lanczos recursions to the 2-D case.