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In this paper, a novel class of normal realizations for discrete-time systems is derived and characterized. It is shown that these realizations are free of self-sustained oscillations and yield a minimal error propagation gain. The optimal realization problem, defined as to find those normal realizations that minimize roundoff noise gain, is solved analytically. Based on Schur-form, a procedure is achieved to obtain the sparse optimal normal realizations. A design example is presented to demonstrate the superior performance of the proposed sparse realizations to several well-known realizations in terms of minimizing the finite precision effects and reducing system implementation complexity.