On the realization of minimum noise and low-noise frequency sampling FIR filters

In this work the finite precision effects issue connected to the frequency sampling realization of FIR filters is considered. In particular, the performance of the frequency sampling filters is evaluated in terms of noise gain for the following three different realizations of the second-order elementary sections: the canonical direct form, the minimum roundoff noise structure, and the suboptimal state-space structure introduced by Bomar. An interesting property on the design of minimum noise second-order sections embedded in the frequency sampling structure, is given. The results obtained show that the realizations via minimum noise structures and Bomar's structures greatly outperform the realizations via canonical direct form structures, and, for very narrow-band filters, have noise gain comparable to that of nonrecursive direct realization.