Improving Harmonic Analysis Using Multitapering: Precise Frequency Estimation of Stellar Oscillations Using the Harmonic F-test
Bibliographic record
Abstract
Abstract In Patil et al., we developed a power spectrum estimation method, mtNUFFT (or multitaper nonuniform fast Fourier transform), for analyzing time series with quasi-regular spacing, and showed that it not only improves upon the statistical issues of the Lomb–Scargle (LS) periodogram, but also provides a factor of 3 speedup in some applications. In this paper, we extend mtNUFFT to include a multitaper F-test, a hypothesis test to assess whether a strictly periodic signal or its harmonic (as opposed to, e.g., a quasi-periodic signal) is present at a given frequency. This extension is possible because the F-test is an accompaniment to the multitaper power spectrum estimator (as opposed to other estimators such as the LS periodogram). The mtNUFFT/F-test combination allows detection of strictly periodic signals embedded in noise and precise estimation of their frequencies, in addition to power spectrum estimation. 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, which opens opportunities to perform detailed investigations of periodic signals in time-domain astronomy.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".