New Z-Domain Continued Fraction Expansions Based on an Infinite Number of Mirror-Image and Anti-Mirror-Image Polynomial Decompositions

A magnitude response preserving modification of the denominator polynomial of a causal and stable digital transfer function leads to an infinite number of decompositions into a mirror-image polynomial (MIP) and an anti-mirror-image polynomial (AMIP). Properties and identifications of the MIP and AMIP are given. The identifications of Schussler and Davis, and the line spectral frequency formulation are special cases of the general MIP and AMIP decompositions introduced in this paper. Two types of Discrete Reactance Functions (DRF) are constructed. From these DRFs, five new continued fraction expansions (CFE) are developed, and some properties are obtained.