A solution is presented for the problem of realizing a discrete-time LTI state-space model of minimal McMillan degree such that its first N expansion coefficients in terms of generalized orthonormal basis match a given sequence. The basis considered. also known as the Hambo basis, can be viewed as a generalization of the more familiar Laguerre and two-parameter Kautz constructions, allowing general dynamic information to be incorporated in the basis. For the solution of the problem use is made of the properties of the Hambo operator transform theory that underlies the basis function expansion. As corollary results compact expressions are found by which the Hambo transform and its inverse can be computed efficiently. The resulting realization algorithms can be applied in an approximative sense. for instance. for computing a low-order model from a large basis function expansion that is obtained in an identification experiment.