The Wold Isomorphism for Cyclostationary

In 1948 H. Wold introduced an isometric isomorphism between a Hilbert (linear) space formed from the weighted shifts of a numerical sequence and a suitable Hilbert space of values of a second order stochastic sequence. Recently W.A. Gardner has resurrected the idea in the context of numerical cyclostationary sequences and processes , but without complete details. In this paper we present the details of the Wold isomorphism between cyclostationary numerical sequences and stochastic sequences. We apply the representations for stochastic CS sequences to the situation of numerical CS sequences. Finally, we show how a numerical CS sequence, from its very deenition, is naturally expressed as a projection of a stationary numerical sequence.