Z-domain continued fraction expansions for stable discrete systems polynomials

A -plane continued fraction expansion (CFE) that is related to the first Cauer -plane CFE via Bruton\´s LDI transformation is considered. Necessary and sufficient conditions are imposed on the CFE for a polynomial to be stable (have all its zeros inside the -plane unit circle). The implementation of this CFE in a tabular form establishes the Routh-like stability table in [1] first derived in a conference paper [2]. The application of this stability table is now extended to also count zeros outside the unit circle, making it compatible in this respect with the related second table form in [3]. However, the closer analogy of the present formulation to the -plane Cauer CFE\´s and Routh table suggest additional merits of this formulation to the design of digital networks (e.g., switched-capacitor filters). A brief account of three related alternative CFE\´s is included.