A fast template periodogram

¹ Department of Astrophysical Sciences, Princeton University, Princeton NJ 08540
² eScience Institute, University of Washington, Seattle, WA 98195

^* jah5@princeton.edu
^** jakevdp@cs.washington.edu
^*** jhartman@astro.princeton.edu
^**** gbakos@astro.princeton.edu

Published online: 8 September 2017

Abstract

This proceedings contribution presents a novel, non-linear extension to the Lomb-Scargle periodogram that allows periodograms to be generated for arbitrary signal shapes. Such periodograms are already known as “template periodograms” or “periodic matched filters,” but current implementations are computationally inefficient. The “fast template periodogram” presented here improves existing techniques by a factor of ∼a few for small test cases (O(10) observations), and over three orders of magnitude for lightcurves containing O(10⁴) observations. The fast template periodogram scales asymptotically as O(HN_f log HN_f + H⁴N_f), where H denotes the number of harmonics required to adequately approximate the template and N_f is the number of trial frequencies. Existing implementations scale as O(N_obsN_f), where N_obs is the number of observations in the lightcurve. An open source Python implementation is available on GitHub.