A note on the periodic Riccati equation and innovations representations of cyclostationary processes

By analogy with the time-invariant case, the difference periodic Riccati equation (DPRE) is related to the solution of the spectral factorization problem for cyclostationary processes. However, in order to associate an innovations-like representation with any periodic solution of the DPRE, positive semi-definiteness of a certain term has to be ascertained. By proving that such a result holds under mild assumptions, a basic result is established in the present work for further development of cyclospectral factorization theory