On the causal factorization problem

The aim of this paper is to analyse the causal factorization problem using the formalism of the infinite zero module and of the infinite pole module introduced in [2]. This enables us to compare different technical solutions of the problem, given in [7] and [5], with the natural conditions, restated in a precise and meaningful sense, which concern the infinite zeros and poles. This approach results in a better understanding of both the problem and the techniques used, in the above mentioned papers, to solve it. Moreover, it allows us to give a characterization, in terms of existence of certain causal factorizations, of the transfer functions having no infinite zeros.