New second-order state-space structures for realizing low roundoff noise digital filters

Several new second-order state-space digital filter structures are introduced. Each of the new structures requires one or two less multiplies than the minimum-noise structure, while achieving a round-off noise performance which is nearly as good. Thus, they provide an excellent means of realizing second-order subfilters. When such subfilters are used to construct nth-order filters, the reduction in multiplies, as compared to using minimum-noise subfilters, is from about 4n to about 3n. An approach to developing simple, algebraic, real-arithmetic design equations for L2-norm scaled second-order structures is presented and then applied to obtaining design equations for the new structures and for the minimum-noise structure.