Some properties of the z-domain continued fraction expansions of 1-D discrete reactance functions

The denominator polynomial of a given causal stable z-domain transfer function is modified so that the magnitude of the frequency response remains the same. This simple modification permits an infinite number of decompositions of the modified denominator into a mirror-image polynomial (MIP) and an anti-mirror-image polynomial (AMIP). Two types of Discrete Reactance Functions (DRF) are constructed. From these DRFs, continued fraction expansions (CFE) are considered and some properties are obtained. These properties indicate whether the original denominator polynomial has all its roots within the unit circle (is minimum phase) or not.