This note deals with the H-infinity filtering, prediction, and smoothing problems for discrete-time linear systems. The J-spectral factorization approach is pursued and, for each of the three problems, a computationally efficient procedure to derive a J-spectral factor is presented. The construction of filter, smoother, and predictor hinges on the stabilizing solution of the same algebraic Riccati equation. This fact allows for the avoidance of any fictitious augmentation of the state-space dimensions.