State-space structures for the realization of low roundoff noise digital filters

The synthesis of computationally efficient low roundoff noise, L(2) norm scaled, state space realizations for fixed point recursive digital filters is studied. In addition to low roundoff noise, such realizations also possess low coefficient sensitivity and low likelihood of sustaining overflow oscillations. The theory of state space structures is reviewed, techniques for synthesizing minimum roundoff noise state space structures are reviewed, techniques for synthesizing minimum roundoff noise state space structures are discussed, and a new technique for synthesizing n(th) order minimum noise structures is introduced. Extension of the technique to state decimation realizations is considered. Two new n(th) order state space structures are proposed. Several new second order filter structures are also introduced. An approach to developing simple algebraic, real arithmetic design equations for scaled second order structures is presented and then applied to deriving design equations for the new structures and for the minimum noise and normal structures.