In this manuscript, a novel algorithm is presented for the identification of single input single output linear time invariant (SISO-LTI) systems. The proposed method is able to find poles of the transfer function describing the system without any assumptions on the system order. The results presented in this paper generalize earlier identification schemes based on expansions of the transfer function using generalized rational orthogonal basis functions (GOBFs). These previous methods depended on a convergent sequence constructed from the coefficients of the orthogonal GOBF expansion. The first contribution of this study is showing that a wider family of functions may be used to construct similar pole finding algorithms. The aforementioned previous approaches can be interpreted as special cases of the results presented here. In addition, using this generalization a new pole identification scheme is proposed using finite Blaschke-products. Through experiments, the practical utility of this scheme is verified when compared to earlier variations of the pole finding scheme.