Roundoff noise analysis of two efficient digital filter structures
Zixue Zhao, Gang Li · IEEE Transactions on Signal Processing · 2006
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 /spl rho/-operator (/spl rho/DFIIt), recently proposed in . The expression of roundoff noise gain is derived, based on which a revised /spl rho/DFIIt structure, denoted as /spl rho/RDFIIt, is obtained. It is shown that the /spl rho/RDFIIt structure, having the same implementation complexity, yields a smaller roundoff noise gain than the /spl rho/DFIIt. The roundoff noise gain for the /spl rho/RDFIIt 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.