A canonical representation of input-balanced realizations for discrete-time systems

In this paper, based on a matrix factorization a novel structure is proposed for digital system implementation and adaptive filtering applications. The equivalent state-space realization of such a structure is an input-balanced realization. Like the normalized lattice structure, it contains a series of Givens rotations. This proposed structure is simpler than the normalized structure and can be implemented very efficiently using the Coordinate Rotation Digital Computer (CORDIC) techniques. This canonical parametrization is particularly important for ensuring the bounded input bounded output (BIBO) stability when used for adaptive filtering. Numerical examples show that the proposed structure outperforms the traditional direct-form II (DFII) structures as well as the normalized lattice structure in terms of minimizing parameter sensitivity and hence roundoff noise.