Recovering dynamically independent coordinates for time-delay-embedded product systems

Phase space embeddings, time-delay or otherwise, do not preserve the natural decoupled description of a product system´s state variables. The authors show, invoking a genericity argument, that for a restricted class of diffeomorphic transformations the images of independent manifolds can be isolated in the embedded phase space without knowledge of the underlying dynamical description. Several applications of this results are suggested, including the separation of signals originating from independent dynamical systems. Some of the estimation problems that must be resolved before this technique realizes its full potential are mentioned.<>