Simplification ofz-transfer functions by continued fractions †

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Abstract
A computer-oriented procedure for the simplification of a z -transfer function is presented. The method consists of (1) transformation of the z-transfer function into the w domain by the bilinear transformation, w=(z− l)/)z+ 1), (2) continued fraction expansion of the w -transfer function into the Cauer second form, (3) keeping the first several quotients and discarding others, (4) converting the truncated continued fraction into z-transfer function of low order. An example is used to illustrate the rapid rate of convergence.

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