Algorithms for expansion and inversion of Davis' z-domain continued fractions

Davis [4] has given an expansion of a function into a continued fraction in terms of the forward difference
z- 1
and the backward difference
1 - z^-1
, functions on an alternating basis. Algorithms, novel and computationally efficient, for implementing this new
z
-domain continued fraction are presented in this brief. These procedures are direct extensions of the algorithms developed earlier for continuous systems [6], [7]. Examples are included.