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According to L. Eyer et al. (1999), the correct Nyquist frequency of irregularly sampled data is

$$ \frac{1}{2p} $$

Where $p$ is the largest value such that:

$$ \forall t_i,t_i = t_1 + n_ip \\ \text{where}~n_i \in \mathbb{N} $$

However, the paper gives no information on how to calculate $n_i$, other than stating that:

$p$ is a kind of greatest common divisor (gcd) for all $(t_i - t_1)$.

Which doesn't really help. So, how does one calculate $p$ or $n_i$ for a given time series. Or, more importantly, is there a better way of calculating the Nyquist frequency of irregularly sampled data?

N.B. That the common methods of taking $p = s$ (the shortest sampling rate in the time series) or $p = \delta s$ (the average sampling rate in the time series) or $p = S$ (the longest sampling rate in the time series) all result in explicable behaviour (as outlined in the paper) -- mainly that super-Nyquist frequencies can be resolved (not through aliasing trickery).

cyphar
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The mathematical statement is saying "p is the largest number such that for all sampling times, the sampling time is equal to the time of the first sample plus an integer multiple of p" this is essentially the greatest common denominator, as the author says. You can also think of it as placing all the sample times on a number line and finding an even spacing of tick marks such that every sample is at a tick mark. The paper mentions a few possible calculation methods and it is not a trivial problem, so I won't go into actually solving for p.

boomboompsh
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