Allpass expansions of digital transfer functions

It is well known that digital allpass filters can be efficiently realised by using lossless structures which possess low sensitivity, low roundoff noise and are free from limit cycles on implementation with finite word-length registers. It is established that every rational transfer function of a stable IIR filter can be expressed as a linear combination of a set of stable first-order allpass transfer functions. This leads to two types of implementation for every stable IIR digital filter in the form of a parallel or cascade connection of first-order allpass sections.