A new method for estimating the power spectrum of gapped data

The problem of estimating the power spectrum of a discrete time series which consists of individual segments separated by long gaps is considered. A maximum entropy approach is used to fill the gaps with a prediction based on the observed data segments. The method is described in detail and two numerical examples are presented to illustrate the application of the algorithm. The results show that accurate estimates of the frequency, amplitude and phase of the sinusoidal components of a noisy, gapped time series can be obtained without the need to interpret a periodogram containing aliased frequencies.