State structures in digital filter configurations—II. reduced and minimal state structures

Abstract

In Part I of this paper we presented a formal procedure for determining the various state structures associated with any given digital network with the dimension of state vector equal to the number of dynamic elements in the network. For noncanonic networks, it is sometimes possible to find state structures with state vectors of reduced and even lowest dimension. Such a state structure is defined to be reduced state structure except for the case where state vector dimension is the lowest possible (the associated state structure is termed minimal). A graph-theoretic procedure for determing the existence of conditions under which a state structure can be simplified is outlined in this part of the paper.