Simultaneous expansion and inversion of the cauer continued fractions of certain transfer functions

The main aim of this paper is to apply Evelyn Frank's algorithm for the continued fraction expansion of a rational transfer function into Cauer's first and second forms. The very essence of the algorithm itself is an inversion procedure for a continued fraction into a sequence of reduced-order rational transfer functions. This algorithmic scheme is well-suited for efficient computerization. However, it has (like its counterpart, the Routh algorithm) one drawback in that it involves divisions. Hence one might encounter rational quantities while working with integer coefficients. To overcome this, the present algorithm is carefully modified in order to compute the elements in a precise fraction-free manner. The time and Markov parameters of the system are also obtained by the orthogonality properties of the corresponding Cauer continued fractions. The specific methods are discussed in detail and illustrated by explicit numerical examples. © 1988 Taylor & Francis Group, LLC.