Two-dimensional delta-operator formulated discrete-time systems: state-space realization and its coefficient sensitivity properties

Abstract

Delta-operator based implementation of one-dimensional (1-D) discrete-time systems has been the focus of considerable research activity because of its superior finite wordlength properties and possibility of addressing both continuous- and discrete-time systems in a unified manner. We investigate its corresponding two-dimensional (2-D) implementation by introducing the delta-operator based counterpart to the Roesser (1975) local state-space model, the corresponding gramians, and the notion of a balanced realization. The computation of the latter and coefficient sensitivity properties of the resulting implementations are also studied.