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Two different methods for extrapolating a given time-limited data sequence have been proposed. The first uses a linear prediction model and the second is based on a bandlimited constraint. In both cases, the extrapolated sequence is constrained to equal the initial data on the given interval and to provide an estimate of the data outside that interval. A high resolution spectral estimate which contains both gain and phase information is then computed from a Fourier Transform of the extrapolated sequence. This paper develops a closed-form expressions for these spectral estimators when the estimates are constrained to be discrete. In this case, relatively simple expressions result which can be used to compare the two methods in a straightforward manner.