# Finding the Nyquist Frequency of Irregularly Sampled Discrete Data

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).