On jointly stationary feedback-free stochastic processes

We consider stationary stochastic vector processes made up of two component processesyandu. 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 spectrumφy u(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.