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 l₂ dynamic range constraint are provided.