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The overflow oscillation problem in fixed-point arithmetic digital lattice filters is considered. Conditions for overflow stability are formulated in the filter K-parameter space for the 2-multiplier and the 1-multiplier lattice filters, using their state-space description. It is found that the 2-multiplier lattice model is overflow stable over a much wider range of K-parameter than the canonical 1-multiplier model, and that the optimal choice of the sign paramethers cm of the latter as proposed by Markel and Gray sometimes makes the filter overflow unstable. However, both lattices are more stable than the direct form realisation.