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Up: Variable stars: Which Nyquist


1 Introduction

When variable stars observations are analyzed, two major problems arise. First, there are constraints on the sampling times. They can't always be chosen, because of weather conditions or other observing restrictions. Secondly, the stars, even if they are periodic, can have an extremely wide range of periods and behaviors. Therefore, astronomers would like to know up to which higher limit it makes sense to search for frequency.

In the literature, there are contradictions regarding the Nyquist frequency for irregularly sampled data. Some authors (Press et al. 1992; Horne et al. 1986) identify it with $1/2\overline{\delta t}$ where $\overline{\delta t}$ is the "average'' sampling rate. The Nyquist frequency is also often identified with $\nu=1/2s$, where s is the smallest time interval in the sample (Scargle 1982; Roberts et al. 1987). Nevertheless, Press et al. (1992) and Roberts et al. (1987) remarked that frequencies can be detected above their quoted values.

For evenly sampled data, the Nyquist frequency is defined as $1/2\delta t$, where $\delta t$ is the time sampling step. We will show how this quantity can be extended to the irregular situation. In most cases, the Nyquist frequency is much larger than usually thought. The present work is particularly relevant to large databases that are becoming available (MACHO, OGLE, EROS, HIPPARCOS, etc.).


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Up: Variable stars: Which Nyquist

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