An equivalent network theory for a class of discrete-time networks

Presented in this paper is an equivalent network theory for linear shift-invariant discrete-time networks having simple poles. Expressions are given for the network transmittance matrices in terms of a decomposition of the network´s rational system function matrix H(z), and a set of arbitrary parameter matrices. Selecting values for the parameter matrices defines a discrete-time network whose system function matrix is H(z). All possible values of these arbitrary matrices define the class of equivalent networks which realize H(z). An important consequence of the theory is that it becomes feasible to synthesize directly the discrete-time structure(s) which are optimum according to a preselected optimization criterion. An example is presented which illustrates the application of the theory in the realization of digital filter structures.