Finite sensor dynamical sampling

Abstract

Dynamical Sampling aims to subsample solutions of linear dynamical systems at various times. One way to model this consists of considering inner products of the form 〈h,Anfi〉, where h is the signal, (fi) a system of fixed vectors and A a linear operator which is connected with the dynamical system. Here, we characterize those systems (Anfi)n∈ℕ, i∈I with finite index sets I and normal operators A which are frames for the underlying Hilbert space. It turns out that this problem is intimately connected with spectral properties of the operator A and complex analysis in the unit disk. We also provide conditions on the spectral properties of A* for non-normal A.