Low-noise structures for narrow-band recursive digital filters without overflow oscillations

Most of the literature dealing with low-noise realizations for narrow-band recursive digital filters is based on the 2AB structure proposed by Agarwal and Burrus. We show that for poles in the neighborhood of the point
z = 1
, i.e., the region where 2AB structures are of interest, it is possible to obtain initial conditions such that any structure based on the 2AB realization will sustain zero-input overflow oscillations for modulo two arithmetic. Alternatives to the 2AB structure are given which are overflow stable, at least, for poles near
z = 1
. Some numerical results are also presented.