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. (C) 2013 Elsevier Ltd. All rights reserved.