Realizing system poles identification on the unit disc based on Laguerre representations and hyperbolic metrics

In a series of paper the authors proposed a new frequency-domain approach to identify poles in discrete-time linear systems. The discrete rational transfer function is represented in a rational Laguerre-basis, where the basis elements are expressed by powers of the Blaschke-function. This function can be interpreted as a congruence transform on the Poincaré unit disc model of the hyperbolic geometry. The identification of a pole is given as a hyperbolic transform of the limit of a quotient-sequence formed from the Laguerre-Fourier coefficients. In this paper the opportunities of reliably computing the poles are analyzed, and some algorithms are proposed for practical use.