On the Estimation of Sinusoidal Parameters Via Parabolic Interpolation of Scaled Magnitude Spectra
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Bibliographic record
Abstract
Sinusoids are widely used to represent the oscillatory modes of music and speech. The estimation of the sinusoidal parameters directly affects the quality of the representation. A parabolic interpolation of the peaks of the log-magnitude spectrum is commonly used to get a more accurate estimation of the frequencies and the amplitudes of the sinusoids at a relatively low computational cost. Recently, Werner and Germain [1] proposed an improved sinusoidal estimator that performs parabolic interpolation of the peaks of a power-scaled magnitude spectrum. For each analysis window type and size, a power-scaling factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> is pre-calculated via a computationally demanding heuristic. Consequently, the power-scaling estimation method is currently constrained to a few tabulated power-scaling factors for pre-selected window sizes, limiting its practical applications. In this article, we propose a method to obtain the power-scaling factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> for any window size from the tabulated values. Additionally, we investigate the impact of zero-padding on the estimation accuracy of the power-scaled sinusoidal parameter estimator.
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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 | 0.000 |
| 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 it