ROM/ACC realization of digital filters for poles near the unit circle

Two all-pole filter structures proposed by Agarwal and Burrus have small roundoff error and coefficient sensitivity for poles near the unit circle. Assuming equal word lengths for input and output, we first give expressions for the mean-squared noise-to-signal
(N/S)
ratios in these structures. We then consider implementation of the Agarwal-Burrus structures using multiplierless ROM-accumulator (ROM/ACC) arithmetic. The
N/S
ratios, including sensitivity considerations, are presented and shown to be small. In addition, limit cycle bounds are given and also shown to be small. An example demonstrates that the new realixations may require as little as one-half the ROM word length and operate at up to twice the word rate of direct form ROM/ACC realizations that achieve the same
S/N
.