Spatial prediction filtering in fractional Fourier domains
Bibliographic record
Abstract
We generalize the time and frequency spatial predictive filtering techniques by means of the fractional Fourier transform. This time‐frequency transform is a generalization of the Fourier transform by introducing a fractional parameter that allows transformation to any of a continuous family of spaces intermediate to the time and frequency domains. The family of fractional Fourier transforms of a signal can be considered as interpolated representations between the signal and its Fourier transform. Prediction techniques, such as spatial prediction filtering, are based on the assumption that the signal to be filtered is composed of two parts: one predictable, the coherent signal and other unpredictable, the random noise. A lateral prediction algorithm estimates the predictable component of a trace from its neighboring traces. In the conventional spatial prediction process, lateral coordinates are always spatial and the vertical coordinate can be either time or frequency. By applying the fractional Fourier transform in the vertical direction we extend the prediction techniques to a continuum of mixed time‐frequency domains in which time and frequency are just particular cases. We test the method in the new domains using stationary a non‐stationary synthetic seismic data.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".