Estimation of sinusoids from incomplete time series

The Gerchberg-Papoulis extrapolation algorithm was applied to the problem of recovering missing observations from incomplete time series. It has been experimentally shown that with as few as 10 percent of data points and a priori information on the bandwidth, it is possible to recover all the missing points in the time series. The technique is illustrated by means of a pair of sinusoids sampled randomly. It has been possible to estimate the entire time series with mean-squaze error less than 0.0035 after 30 iterations. The parameters of the sinusoids could be estimated with high accuracy.