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 \ninstantaneous 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 \nto a solar time series from the GOLF SoHO instrument.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 teacher head, 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".