Estimate of aliasing error for non-smooth signals prefiltered by quasi-projections into shift-invariant spaces
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Bibliographic record
Abstract
An ideal analog-to-digital (A/D) converter prefilters a signal by an ideal lowpass filter. Recent research on A/D conversion based on shift-invariant spaces reveals that prefiltering signals by quasiprojections into shift-invariant spaces provides more flexible choices in designing an A/D conversion system of high accuracy. This paper focuses on the accuracy of such prefiltering, in which the aliasing error e/sub f//sup /spl lambda// is found to behave like e/sub f//sup /spl lambda// /sub 2/ = O(/spl lambda//sup -/spl alpha//) with respect to the dilation /spl lambda/ of the underlying shift-invariant space, provided that the input signal f is Lipschitz-/spl alpha/ continuous. A formula to calculate the coefficient of the decay rate is also figured out in this paper.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 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.
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