A New Z Domain Continued Fraction Expansion

A new domain continued fraction expansion is presented which proceeds in terms of and factors. It is proved to be always convergent for polynomials whose roots all lie within the unit circle. The procedure involves a unique decomposition of the given polynomial into a mirror image polynomial (MIP) and an antimirror image polynomial (AMIP) whose degrees differ by unity. The ratio of these polynomials is shown to possess the properties of a digital reactance function. The continued fraction expansion developed here-due to the fact that and are the inverse transmittances of digital accumulators, as well as of switched capacitor integrators-has application to the synthesis of digital and switched capacitor ladder filters.