A unified framework for the realization problem in linear digital filtering

In a new approach to characterizing the implementation of linear digital filters all possible realizations for any filter are treated in the same framework, based on the representation of an input/output specification for a linear filter by a unique, possibly infinite transmission matrix, which can be extended to include arrays of higher than two dimensions or of arbitrary dimensions. A set of notations and operation rules for these arrays and matrices is presented, and all possible implementations of a filter are characterized as factorizations of its transmission array.