NON-MINIMAL REALIZATIONS OF FIXED-POINT DIGITAL FILTERS THAT ARE FREE OF ALL FINITE WORD-LENGTH LIMIT CYCLES.

Every linearly stable, fixed-point digital filter has a realization, using standard two's complement arithmetic with rounding, that will be free of all autonomous finite-word limit cycles. Specific structures that will achieve this condition, consisting of combinations of transversal structures and recursive structures, are derived using a state-space formalism. Freedom from limit cycles is obtained by a design procedure that reduces the norm of the matrix in the recursive feedback loop.