Laguerre z-transfer function representation of linear discrete-time systems

In this paper, the difference equation of a linear discrete-time dynamical system is transformed into a rational function, which is called the ‘Laguerre z-lransfer functio’. This function is obtained from the ratio between the z-transform of the Laguerre spectrum of the output and the corresponding transform of the spectrum of the input. Simple formulas for transforming the original system into the Laguerre system, and vice versa, are derived. Interesting properties of the Laguerre z-transfer function representation are also given. This representation is then applied to the identification of models of SISO discrete-time systems from input-output data