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

High frequency limits in periodicity search from irregularly spaced data