Stationary random processes forming frames and basis: Some applications

We will give necessary and sufficient conditions for {X
_k

ⁿ
}
_kisinZopf

^n=1...N
the samples taken at uniform rate from a w.s.s. processes (or of an ldquoobservedrdquo process) to form a frame or a Riesz basis of its span. In some way this is an analogue problem to that of finding conditions for frames of a shift invariant subspace of L
²
(Ropf) with a finite number of generators. We will give also related results and applications.