A General Description of Linear Time-Frequency Transforms and Formulation of a Fast, Invertible Transform That Samples the Continuous S-Transform Spectrum Nonredundantly
Why this work is in the frame
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Bibliographic record
Abstract
Examining the frequency content of signals is critical in many applications, from neuroscience to astronomy. Many techniques have been proposed to accomplish this. One of these, the S-transform, provides simultaneous time and frequency information similar to the wavelet transform, but uses sinusoidal basis functions to produce frequency and globally referenced phase measurements. It has shown promise in many medical imaging applications but has high computational requirements. This paper presents a general transform that describes Fourier-family transforms, including the Fourier, short-time Fourier, and S- transforms. A discrete, nonredundant formulation of this transform, as well as algorithms for calculating the forward and inverse transforms are also developed. These utilize efficient sampling of the time-frequency plane and have the same computational complexity as the fast Fourier transform. When configured appropriately, this new algorithm samples the continuous S-transform spectrum efficiently and nonredundantly, allowing signals to be transformed in milliseconds rather than days, as compared to the original S-transform algorithm. The new and efficient algorithms make practical many existing signal and image processing techniques, both in biomedical and other applications.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| 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