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The concept of a finite-state machine (FSM) is used in an attempt to cover the deficiencies of the conventional digital filter design procedure with respect to finite-word-length effects. The problem of synthesis is considered in detail and a procedure whereby the FSM mappings are designed to best model a given difference equation is presented. This procedure is based on a well known graph theory algorithm. The FSM digital filter design procedure is evaluated by computer simulation of various small-word-length filters. Several examples are presented to demonstrate the improved performance of the FSM filters with respect to conventional fixed-point designs. The design procedure also allows the construction of limit-cycle-free high-order direct-form filters. This form is compared to the more conventional cascade structure.