Roundoff noise analysis of two efficient digital filter structures

In this correspondence, two efficient structures are analyzed for the implementation scheme of rounding before multiplication (RBM). The first one is the direct-form II transposed structure in ρ-operator (ρDFIIt), recently proposed in . The expression of roundoff noise gain is derived, based on which a revised ρDFIIt structure, denoted as ρRDFIIt, is obtained. It is shown that the ρRDFIIt structure, having the same implementation complexity, yields a smaller roundoff noise gain than the ρDFIIt. The roundoff noise gain for the ρRDFIIt structure with error feedbacks is also derived. Each structure can be optimized with regard to the free parameters it possesses with a genetic algorithm. Numerical examples are presented, which show that the optimized structures are very competitive because they can even outperform the traditional optimal state-space realization in terms of the roundoff noise performance as well as the implementation simplicity.