Design of stable adaptive recursive filters using a new parametrization of 2nd order balanced realizations

A new characterization of input-balanced realizations is derived for 2nd order filters, based on which a filter structure is proposed. Like the normalized lattice structure, the stability of the proposed structure can be ensured in a time-varying environment and has a much better behavior in terms of signal dynamic range than the direct-form II structure. Compared with the normalized lattice structure, it is more efficient. Based on this structure, an adaptive filter is derived. The results can be extended easily to any filter by cascading the denominator of the filter transfer function with a set of 2nd-order sub-filters that are implemented with the proposed structure. Extensive simulations are given to support the theoretical results and to compare the performance of the proposed structure with that of the classical direct-form II structure.