factorizations of a general discrete-time system

The problems of extending the J -lossless conjugation, the ( J , J ′ ) -spectral factorization, and the ( J , J ′ ) -lossless factorization to a completely general discrete-time system are considered. Existence conditions together with a numerically-sound prototype algorithm for computing the factors are provided for a system having any type of singularity, including arbitrary normal rank, poles and zeros at infinity, at zero, or on the unit circle.