Stable reduction of linear discrete-time systems via multipoint squared-magnitude CFE

Abstract

This paper presents an elegant and computer-oriented procedure for the stable reduction of a linear discrete-time system via a multipoint continued-fraction expansion of its z-transfer function G(z). The proposed procedure involves the following three steps: (a) transform the z-domain squared-magnitude function P(z) = G(z)G(z −1) of the system frequency response to P(u) by the transformation u = z + z −1; (b) obtain an mth-order multipoint continued-fraction approximant Pm (u) to P(u); (c) factorize Pm (u) to yield a reduced z-transfer function Gm (z). The main feature of the procedure is that it guarantees the stability as well as the minimum-phase characteristics of the system and it also gives good overall approximations to both frequency and time responses.