Sampling Rate

A reader recently asked:

T, from my mechanical engineering world we have strict rules on sampling rates vs. signal frequency rates. Ie you cannot reliably measure a 60hz ac sine wave with a 5hz analog sampling device. The result ends up being strange results that don’t show spikes well and also might not show averages well either. Can you help me understand how 120 year sampling proxies can resolve relatively high frequency temperature spikes?

This objection comes up so often from those who are accustomed to data which are evenly sampled in the time domain, and the misconception is so firmly imprinted on so many people, that it’s worth illustrating how uneven time sampling overcomes such limitations.

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Skin a Cat

Before I begin let me make it clear that this is not about abusing cats. I love cats. We have a cat. We treat him very well. He treats us as though it’s our duty to worship him. He’s a cat.

This is about the old adage that “there’s more than one way to skin a cat.”

Seeing the Light

These days, amateur astronomers are far better equipped — at least electronically — than they were just a decade ago. Many of them have acquired CCD cameras at modest expense and have learned well how to use them to estimate the brightness of variable stars, a process called CCD photometry. This makes for more precise measurements than the “old way,” which was to look at the star, possibly assisted by a telescope or binoculars, but with no other instrument to estimate brightness than the human eye. The target star is compared to nearby stars of known brightness (comparison stars) and a “judgement call” is made. This process is called visual photometry.

Through a Picket Fence

Suppose you’re an astronomer interested in variable stars — stars which change brightness. You decide to collect some data on the brightness of a newly discovered variable. It never gets brighter than magnitude 9, which is too faint to be detected with the naked eye, but you’re at a major observatory so that’s no problem. You have access to, and training in the use of, high-precision CCD photometry so your data will be outstanding. Of course, you can only see it at night and there’s stiff competition for observing time on the observatory telescope, but you manage to schedule regular observations at precisely midnight every 16 days for slightly over a year.