Multitaper Statistical Tests for the Detection of Frequency-Modulated Signals
Bibliographic record
Abstract
Detection of periodic signals in noise is an important problem in many scientific fields and there exist tools in the multitaper spectrum estimation and harmonic analysis framework for doing so, for example, the Harmonic F statistic. However, the Harmonic F statistic can lose effectiveness under certain types of frequency modulation, when the signal to noise ratio is low, and when the background spectrum is highly coloured. In his 2009 paper, "Polynomial Phase Demodulation in Multitaper Analysis," Thomson proposed methods for dealing with time series data (specifically, solar data) where these problems are present. In this thesis we propose an extension of this work to deal with the detection of frequency modulated signals. The method uses the Slepian sequences as projection filters to reconstruct the series based on a 2W band around a given carrier frequency and then tests the instantaneous frequency series for a low-degree polynomial form in that band using the Slepians combined with an associated family of polynomials in a variance ratio test statistic. Under the null hypothesis that there are no sinusoidal signals with polynomial frequency modulation at the given carrier frequency, these test statistics are approximately distributed according to an F distribution with degrees of freedom depending on the number of tapers used and the degree of the polynomial being tested. We compare several such test statistics via simulation studies and apply them to a solar time series from the GOLF SoHO instrument.
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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 | 0.016 | 0.087 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".