This work deals with the identification of dynamic systems from noisy input-output observations, where the noise-free input is not parameterized. The basic assumptions made are (1) the dynamic system can be modeled by a (discrete- or continuous-time) rational transfer function model, (2) the temporal input-output disturbances are mutually independent, identically distributed noises, and (3) the input power spectrum is non-white (not necessarily rational) and is modeled nonparametrically. The system identifiability is guaranteed by exploiting the non-white spectrum property of the noise-free input. A frequency domain identification strategy is developed to estimate consistently the plant model parameters and the input-output noise variances. The uncertainty bound of the estimates is calculated and compared to the Cramer-Rao lower bound. The efficiency of the proposed algorithm is illustrated on numerical examples. (C) 2013 Elsevier Ltd. All rights reserved.