The paper presents a new method for all-pole model estimation based on minimization of the weighted mean square error in the sampled spectral domain. Due to discrete nature of the proposed distance measure, emphasis can be put on an arbitrary set of spectral samples what can greatly improve the model accuracy for periodic signals. Weighting can also be applied to improve the fitting in certain spectral regions according to any desired fidelity criterion. Iterative algorithm for determination of the optimal model is proposed and an exceptionally fast convergence rate is demonstrated. Accuracy of the estimation algorithm is verified on an example of a synthetic vowel for a broad range of pitch frequencies.