Abstract Gaps in observational time series due to factors beyond our control are habitually considered as a nuisance, since they make the spectral analysis of the time series much more complicated as compared with the case of regular observations. Nonetheless, in some applications the gaps may be found useful. It is shown that the spectral analysis of a multi-harmonic function given at two intervals, separated by a gap, yields the results very much similar to those which one has in the case of two antennas connected as an interferometer. This analogy leads to a conception of the Time Interferometer, which in some cases is superior to regular observations since it (a) makes the spectral lines sharper, (b) separates two close harmonics at the cost of sufficient reductions of time and observational expenditures, (c) improves the low frequency problem. This paper presents a theoretical foundation of the Time Interferometer and its application to astrometric time series.