{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/improving-harmonic-analysis-using","title":"Improving Harmonic Analysis using Multitapering: Precise frequency estimation of stellar oscillations using the harmonic F-test","arxiv_id":"2405.18509","date":"2024-05-28","proceeding":null,"authors":["Aarya A. Patil","Gwendolyn M. Eadie","Joshua S. Speagle","David J. Thomson"],"abstract":"In Patil et. al 2024a, we developed a multitaper power spectrum estimation method, mtNUFFT, for analyzing time-series with quasi-regular spacing, and showed that it not only improves upon the statistical issues of the Lomb-Scargle periodogram, but also provides a factor of three speed up in some applications. In this paper, we combine mtNUFFT with the harmonic F-test to test the hypothesis that a strictly periodic signal or its harmonic (as opposed to e.g. a quasi-periodic signal) is present at a given frequency. This mtNUFFT/F-test combination shows that multitapering allows detection of periodic signals and precise estimation of their frequencies, thereby improving both power spectrum estimation and harmonic analysis. Using asteroseismic time-series data for the Kepler-91 red giant, we show that the F-test automatically picks up the harmonics of its transiting exoplanet as well as certain dipole ($l=1$) mixed modes. We use this example to highlight that we can distinguish between different types of stellar oscillations, e.g., transient (damped, stochastically-excited) and strictly periodic (undamped, heat-driven). We also illustrate the technique of dividing a time-series into chunks to further examine the transient versus periodic nature of stellar oscillations. The harmonic F-test combined with mtNUFFT is implemented in the public Python package tapify (https://github.com/aaryapatil/tapify), which opens opportunities to perform detailed investigations of periodic signals in time-domain astronomy.","url_abs":"https://arxiv.org/abs/2405.18509v1","url_pdf":"https://arxiv.org/pdf/2405.18509v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"improving-harmonic-analysis-using","repo_url":"https://github.com/aaryapatil/tapify","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}