New IIR digital filter realizations using residue-feedback

The problem of synthesizing finite wordlength fixed-point realizations of Nth-order IIR digital filters, which use second-order residue feedback, is considered. It is shown that by proper choice of simple residue feedback schemes, new optimal and suboptimal (with respect to output roundoff noise) structures can be obtained for narrow band-pass and band-stop filters. The resulting realizations have full state-space matrices and may provide lower output roundoff noise than those of the optimal realizations proposed by Mullis, Roberts and Hwang. Alternatively, suboptimal realizations with residue feedback and Hessenberg state-space matrices for narrow-band IIR filters are also proposed. These realizations lead to near-optimal roundoff noise and have a saving of N(N -1)/2 multiplies over the optimal ones.