State-structures and minimal state-structures for arbitrary digital filters

This paper presents a formal procedure for determining the state space representations of any digital network consisting of adders, multipliers and delays. Such representations are called state-structures whenever the state variables are exclusively identified to the appropriately chosen internal node variables of the network. In general, the state-structures corresponding to a given network are not unique, and for non-canonic networks, it is sometimes possible to find state-structures for state vectors of the lowest dimension. Procedures for determining such minimal structures are also discussed.