It was old-school-applied-math day at Camp Hogg today, with Itay Yavin (McMaster, Perimeter), Foreman-Mackey, and I talking about how to very quickly find periodic but anharmonic signals in time-series data. We are thinking about Kepler of course, and we are taking brute-force approaches. Our key realization this week, however, has been that if you can make a Fourier Series approximation to the signal you are looking for, then "dot products" or overlap integrals of the data with sinusoids become sufficient statistics for signal detection. This brings down computational complexity by one factor of the size of the data from whatever you had before. Of course we are only thinking about algorithms that work on irregularly sampled data with heterogeneous noise properties; things get even easier if you have uniformly sampled data.
By the way, in a strict technical sense, even if the Kepler satellite takes data at a regular rate according to its on-board clock, the data are not regularly sampled from the point of view of a barycentric or inertial observer for any star. So there are no regularly sampled data sets! This is similar to my oft-stated point that there are no data sets that have no missing data. We have to suck it up. I, for one, am ready to suck.
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