Precise pole realization by unobservable digital filters

In this paper a new filter structure that allows precise pole realization at a variety of locations inside the unit circle is developed and its performance investigated. The proposed structure is based on the ides of augmenting the system to a higher order unobservable filter whose poles are obtained precisely while keeping the multipliers realizable within the given word-length. The additional undesirable poles that result from this augmentation are cancelled approximately by zeros. This results from the fact that the poles are precise and the perturbation is confined to the zeros while the minimal order filter suffers from perturbation of its poles. The unobservable structure is of particular significance for poles either near or on the unit circle where sensitivity to perturbation is high.