Roundoff noise results on optimal and block-optimal digital filter structures

Roundoff noise results of different filter kinds (elliptic, Chebyshev and Butterworth) realized with optimal state-space structures against block-optimal structures are presented. The results are given for fixed-point arithmetic, but they can be extended to the floating-point case. If double-precision accumulators are used, the optimal structure always has lower roundoff noise power than block-optimal structures, but the later have less operations than the former. If single-precision accumulators are used, the block-optimal structure can be less noisy than the optimal one in some cases, and the difference increases with filter order