Distortion rate function of cyclo-stationary Gaussian processes

An expression for the distortion rate function of cyclostationary Gaussian processes is derived. This expression is given by water-filling over the eigenvalues of a spectral density matrix associated with the source. For processes in continuous time, the distortion rate function is given in terms of a limiting function of the eigenvalues of this matrix. A lower bound on the distortion-rate function, which does not involve eigenvalue computation, is also derived. This distortion rate function is evaluated for the processes obtained by modulating a Gaussian stationary narrowband pulse by a deterministic sine wave, and is shown to be equal to the distortion rate function of the stationary narrowband pulse.