An algorithm for extraction of periodic signals from sparse, irregularly sampled data

Temporal gaps in discrete sampling sequences produce spurious Fourier components at the intermodulation frequencies of an oscillatory signal and the temporal gaps, thus signiflcantly complicating spectral analysis of such sparsely sampled data. A new fast Fourier transform (FFT)-based algorithm has been developed, suitable for spectral analysis of sparsely sampled data with a relatively small number of oscillatory components buried in background noise. The algorithm’s principal idea has its origin in the so-called \clean" algorithm used to sharpen images of scenes corrupted by atmospheric and sensor aperture efiects. It identifles as the signal’s \true" frequency that oscillatory component which, when passed through the same sampling sequence as the original data, produces a Fourier image that is the best match to the original Fourier map. Unlike the clean algorithm, it performs the search in the Fourier space. The algorithm has generally met with success on trials with simulated data with a low signal-to-noise ratio, including those of a type similar to hourly residuals for Earth orientation parameters extracted from VLBI data. For eight oscillatory components in the diurnal and semidiurnal bands, all components with an amplitude-noise ratio greater than 0.2 were successfully extracted for all sequences and duty cycles (greater than 0.1) tested; the amplitude-noise ratios of the extracted signals were as low as 0.05 for high duty cycles and long sampling sequences. When, in addition to these high frequencies, strong low-frequency components are present in the data, the low-frequency components are generally eliminated flrst, by employing a version of the algorithm that searches for noninteger multiples of the discrete FFT minimum frequency.