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We have outlined a synthesis procedure which minimizes the output noise in cascade and parallel connections of second-order sections caused by roundoff of internal storage registers. Theorem 1 characterizes the optimal fi Iter and dictates the synthesis procedure. The output noise is made up of two terms. The dominant noise term for block optimal fi lters is independent of bandwidth unl ike the usual cascade and paralle I connections of second-order di rect forms. For narrow band filters improvements of 30 to 40 db are not uncommon. Numerical results yield excellent agreement between theory and simulation.