Low-noise realizations for narrow-band recursive digital filters

Agarwal and Burrus have proposed two all-pole digital filter structures which exhibit very small error for poles near the unit circle. ROM-accumulator (ROM/ACC) implementations of these structures have also been shown to have small error. We extend these resuits by including zeros in both the Agarwal-Burrus structures and their ROM/ACC counterparts. A modified approach toward scaling and selecting various wordlengths is required. Expressions for MSE and bounds on zero input limit cycles are derived for the new structures and shown to be small. As a consequence, the new pole-zero structures can offer significant hardware and speed advantages as illustrated by example.