Spectrum estimation of time series with missing data

In several practical situations involving the estimation of sinusoids from time series, the data available is not complete due to missing data points. The Gerschberg-Papoulis extrapolation algorithm, originally used for the extrapolation of band-limited signals is used for the estimation of the spectrum from incomplete time series. The use of this algorithm is studied for cases where the spectrum of the original signal contains only a discrete set of frequencies, as well as situations where the spectrum is continuous. The algorithm is studied for several cases involving different sampling frequencies and various proportions of missing data points. It is shown that the effectiveness of the algorithm depends on the ratio of the average number of data points available per second to the frequency of the sinusoids involved.