A Structural View of Stability in Adaptive IIR Filters

This correspondence deals with the stability issue in adaptive IIR filters from a structural view. A new condition, under which the bounded-input bounded-output (BIBO) stability of the filters can be ensured, is derived. Based on this result, a normal state-space realization for second-order IIR filters is proposed. It is shown that the adaptive IIR filter realized with such a structure is BIBO stable no matter it is implemented with infinite or finite precision. This property is very important for real-time applications. Though both the proposed and the normalized lattice-based structures are BIBO stable, the former is simpler and has minimal pole sensitivities. Two adaptive IIR filter structures are developed based on a cascade form of second-order filters. The first structure is fit for the filters whose poles are all complex and the second one is for the constrained notch filters. Simulations are given to demonstrate the performance of the proposed structures