On the causal factorization problem

In this note the formalism of the infinite zero module and of the infinite pole module is used to analyze the causal factorization problem. This allows us to express its solutions in terms of zeros and poles at infinity and to have a better understanding of both the problem and the techniques previously proposed by various authors to solve it. Moreover, we obtain a characterization, in terms of the existence of certain causal factorizations, of the transfer functions having no infinite zeros.