Proper elimination of latent variables

We consider behaviors in which we distinguish two types of variables, manifest variables, the variables that are of interest to the user and latent variables, the variables that are introduced to obtain a first representation. The problem is to find a representation of the manifest behavior, that is, we want to eliminate the latent variables. If the original behavior can be represented by linear differential equations with constant coefficients, then under certain conditions the same is true for the manifest behavior. In this note we formulate and study these conditions. The results are illustrated by means of some examples. As an application we study behaviors in image representation.