  The measurement of the betatron tunes in a circular accelerator is of
paramount importance due to their impact on beam dynamics. The resolution of
the these measurements, when using turn by turn (TbT) data from beam position
monitors (BPMs), is greatly limited by the available number of turns in the
signal. Due to decoherence from finite chromaticity and/or amplitude detuning,
the transverse betatron oscillations appear to be damped in the TbT signal. On
the other hand, an adequate number of samples is needed, if precise and
accurate tune measurements are desired. In this paper, a method is presented
that allows for very precise tune measurements within a very small number of
turns. The theoretical foundation of this method is presented with results from
numerical and tracking simulations but also from experimental TbT data which
are recorded at electron and proton circular accelerators.
