Comparative study of the generalized DFIIt structure and its equivalent state-space realization

The generalized direct-form II transposed (DFIIt) structure in δ-operator has been studied by several authors recently and it has been shown that this structure has some nice numerical properties over that in the conventional shift operator. Noting that the δ-operator based DFIIt structure yields a better performance only for those digital IIR filters whose poles are clustered around z = +1, based on a polynomial operator approach a more generalized DFIIt structure is derived and its equivalent state-space realization is investigated in this paper. The corresponding expression for roundoff noise gain is derived. The optimal polynomial problems are then formulated and solved for any given filter. It is shown that this realization yields a smaller roundoff noise gain than that of the generalized DFIIt. A numerical example is given to illustrate the design procedure.