A Kronecker rank theorem for two-dimensional non-causal systems

Abstract

A novel Hankel theory is developed for non-causal multidimensional linear shift invariant systems. It is shown that the rank of a generalized Hankel operator is related in a fundamental way to the rationality of a multidimensional system's transfer function. This theorem may be viewed as a generalization of Kronecker's ID theorem. These results suggest a new algorithm for multidimensional system identification from impulse response measurements.