Median method for robust and accurate power spectral density estimation of stochastic oscillators
Bibliographic record
Abstract
A method is proposed for estimating the power spectral density (PSD) of time series that uses median smoothing in the frequency domain. The "Median method" for PSD estimation rejects deterministic noise peaks in the PSD while preserving stochastic signals and noise sources. For a PSD averaging factor M, deterministic noise sources are suppressed by a factor of ∼M in power when applying the Median method. In addition, the Median method leads to a reduction of spectral leakage by a factor of ∼M relative to traditional methods. An increase of up to 44% in the standard deviation in the PSD estimate from the Median method is the trade-off for these advantages. In the context of a stochastically driven simple harmonic oscillator, the estimation of its parameters (stiffness, Q factor, and resonance frequency) using the Median method is much more robust against the presence of deterministic noise peaks and more accurate than linear PSD estimation methods.
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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 | 0.001 | 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".