On Jointly Stationary Feedback-Free Stochastic Processes

We consider stationary stochastic vector processes made up of two component processes y and u. Such processes arise, for example, in feedback processes. We consider the task of determining whether there is feedback from one process, say, y, to the other, say, u. A definition is proposed for the absence of feedback in terms of the spectrum Φyu(z) of the joint process. Comparison with previous results on feedback-free processes shows that the proposed definition has some desirable properties which were absent in previous work. In particular, system structures other than canonical ones are shown to be feedback-free.