On a generalized factorization problem for structurally passive synthesis of digital filters

The problem of structurally passive synthesis of multidimensional digital filters of the quarter-plane causal type as an interconnection of more elementary building blocks directly in the discrete domain is addressed by means of the factorization of the chain matrix, the hybrid matrix and the transfer function matrix associated with a prescribed multidimensional lossless two-port. By using recent results on the discrete domain representation of such matrices, a generalized lossless two-port matrix is introduced to present all three factorizations in a unified setting. Necessary and sufficient conditions for factorability as well as an algorithm for computing these factors when they exist are obtained. In particular, it is shown that, in one dimension the factorizations can always be performed. Thus, in one dimension, a discrete domain algorithm for synthesizing previously unpublished internally passive structures and alternative methods of synthesis for more conventional structures such as the cascade structure are also obtained