Nonminimal 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. Specific design relations for minimizing the roundoff noise in the presence of an l2dynamic range constraint are provided.