Exact Fractional-Order Differentiators for Polynomial Signals
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Bibliographic record
Abstract
A discrete-time fractional-order differentiator is modeled as a finite-impulse response (FIR) system. The system yields fractional-order derivatives of Riemann-Liouville type for a uniformly sampled polynomial signal. The computation of the output signal is based on the additive combination of the weighted outputs of N cascaded first-order digital differentiators. For differentiators of fractional order with a terminal value equal to zero, the weights are time-varying. The weights are obtained in a closed form involving the Stirling numbers of the first kind. The system tends to a time-invariant integer-order differentiator when the order of the derivative tends to an integer value. It yields exact fractional- or integer-order derivatives of a sampled polynomial signal of a certain order.
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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