Design considerations for very low sensitivity and very low round-off noise recursive digital filters

Sensitivity and round-off noise expressions for recursive fixed point digital filters are presented. These expressions can be used as design aids for the design of low-sensitivity and low-round-off noise recursive digital filters. The sensitivity and round-off noise analysis is carried out for four recursive topologies claimed to be low-sensitivity and/or low-round-off-noise topologies. The results show that, if one is looking only for a low sensitivity filter, the best one is the Agarwal-Burrus structure. But if one is looking for a low-round-off-noise structure for poles close to |z| = 1, the best one is the Nishimura-Hirano-Pal structure. For poles not close to the unit circle, the Agarwal-Burrus structure is superior in terms of round-off noise and sensitivity to coefficient wordlength