New recursive digital filter structures having very low sensitivity and roundoff noise

For poles close to the unit circle and near
z = 1
, the usual realizations of recursive or IIR digital filters are highly sensitive to the coefficient quantization and have large roundoff noise. As the sampling rate is increased the poles approach
z = 1
and the problems become more severe. For these situations several new digital filter structures are presented for which the above errors remain constant and generally insignificant as the sampling rate is increased. Results on sensitivity and the roundoff errors for these new structures are presented and compared with conventional realizations. Some numerical results are also presented showing order of magnitude improvements.