An Efficient and Robust Orthogonal Structure for Linear Discrete-Time Systems

Abstract

An orthogonal structure is derived for system implementation. The expression of roundoff noise propagation gain for this structure is obtained. The proposed structure is an improved version of that reported in the paper by G. Li, M. Gevers, and Y.X. Sun (Performance analysis of a new structure for digital filter implementation, IEEE Trans. Circuits Syst. I 47:474–482, 2000), but is more efficient and robust against the quantization errors. For comparison, an alternative expression of roundoff noise gain for the normalized lattice structure is derived, based on which it is shown that the roundoff noise gain of an Nth order all-pass system, when implemented using the normalized lattice structure, is 4N and that an Nth order system implemented with the structure proposed in the paper by P.P. Vaidyanathan, S.K. Mitra, and Y. Neuvo (A new approach to the realization of low sensitivity IIR digital filters, IEEE Trans. Acoust. Speech Signal Process. ASSP-34(2):350–361, 1986), yields a roundoff noise gain of N+1, smaller than that of the classical optimal roundoff noise state-space realizations. Design examples are presented to illustrate the behavior of the proposed structure and to compare it with a class of existing orthogonal structures and the classical optimal roundoff noise realizations. It is shown that the proposed structure outperforms the others in terms of minimization of roundoff noise as well as implementation efficiency.