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The problem of estimating the frequencies, dampings, amplitudes and phases of closely spaced complex damped exponentials in the presence of noise is considered. In several papers, decimation is proposed as a way to increase the performance of subspace-based parameter estimation methods, in the case of oversampling. In this paper, a novel extension of the HTLS-method (Hankel-Total Least Squares) that operates directly on the decimated data matrix is presented, and it is compared to other decimation methods. Experiments on simulated nuclear magnetic resonance (NMR) spectroscopy signals show the influence of decimation on the accuracy and computational complexity of the estimators.