Stable Reduction of Linear Discrete-Time Systems Via a Multipoint Tangent Phase CFE

This paper presents a procedure of linear discrete-time system reduction via a multipoint tangent phase continued-fraction expansion (CFE). The model reduction approach followed starts by transforming the z-domain tangent phase function into the u-domain one using the u-transformation u = z⁻¹ + z. Subsequently, the u-domain tangent phase function is expanded into a multipoint continued fractions. The desired reduced z-transfer function is finally obtained by factorizing the truncated and inverted u-domain multipoint tangent phase CFE approximant. The main feature of the proposed method is that it not only guarantees the stability but also gives good overall approximations to both frequency and time responses of the given system.