High frequency limits in periodicity search from irregularly spaced data

Notions and limits from standard time series analysis must be modified when treating series which are measured irregularly and contain long gaps. Classical Nyquist criterion to estimate frequency range which is potentially recoverable must be modified to handle this more complex situation. When basic exposition of the modified criterion is given in earlier papers, some minor problems and caveats are treated here. Using simple combinatorial arguments we show that for small sample sizes the modified Nyquist limit may overestimate the obtainable frequency range. On the other hand we will demonstrate that very high Nyquist limit values which are typical to irregularly sampled data can often be taken seriously and using proper observational techniques the frequency ranges for "time spectroscopy" can be significantly widened.