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 Poincaŕe 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. This paper extends this approach by defining an iterative procedure to explore the pole structure. This is based on the successive elimination of the already identified poles by using the Malmquist-Takenaka representation of the discrete transfer function. The proposed procedure is suitable not only for structure estimation with no need of a priori assumption on the pole locations but knowing the poles it serves also as a basis for linear estimation of the residues or numerator coefficients in a rational orthogonal basis.