Optimal structures for high speed and low roundoff noise digital filters

The authors propose the optimization of the parallel and cascade connections of second-order sections, by selecting the best section for realizing each pair of complex-conjugate poles (and zeros). The optimization sense is, first, the minimization of the output roundoff noise and power and, second, the minimization of the number of operations. The optimal second-order state-space section is the realization for those poles close to z=1 (or -1) and the second-order direct section for poles far from z=±1. These results are almost independent of the filter transfer function. Experimental results with Butterworth, Chebyshev, and elliptic filters are given to support the theory