A New Look at Frequency Resolution in Power Spectral Density Estimation
Bibliographic record
Abstract
The problem of frequency resolution in non-parametric power spectrum density estimation (PSDE) for noisy signals is considered. In this setting, finite length of data as well as the additive noise, both contribute to a decreased frequency resolution. The existing PSDE approaches offer different forms of averaging and windowing of the available data only to improve statistical properties of the estimates, however, at the expense of reducing frequency resolution. In these approaches, the additive noise and the finiteness of data which are the causes of the original loss of the frequency resolution are not treated separately. In this paper, we suggest a new approach which takes advantages of these two different causes of the problem. Therefore, the new nonparametric approach to spectrum estimation tackles the problem of resolution in two steps. First, the method optimally reduces noise interference with the signal via minimum noiseless description length (MNDL). The new power spectrum estimation MNDL-periodogram (PMNDL) of the denoised signal is then computed via conventional indirect periodogram to improve frequency resolution
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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 | 0.006 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.002 | 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".